1 /*
2 * $Id$
3 *
4 * Created on 26 Jan 2010 by Paul Harrison (paul.harrison@manchester.ac.uk)
5 *
6 * Adapted from official SOFA C implementation http://www.iausofa.org/
7 */
8
9 package org.jastronomy.jsofa;
10
11 import static java.lang.StrictMath.*;
12
13 /**
14 * Java implementation of Standards of Fundamental Astronomy. <a href="http://www.iausofa.org/">http://www.iausofa.org/</a>
15 *
16 * This code has been created by hand translating the official C version.
17 *
18 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 02 Apr 2014
19 * @version JSOFA Release 2016-07-29_a
20 * @since 26 Jan 2010
21 */
22 public class JSOFA {
23 /** tracked IAU SOFA release {@value}. */
24 public final static String SOFA_RELEASE = "2016-07-29";
25
26 /** tracked IAU SOFA revision {@value}. */
27 public final static String SOFA_REVISION = "12";
28
29
30
31 /** Seconds of time to radians {@value} */
32 public final static double DS2R = (7.272205216643039903848712e-5);
33
34 /** Pi {@value}*/
35 public final static double DPI = (3.141592653589793238462643);
36
37 /** 2Pi {@value}*/
38 public final static double D2PI = (6.283185307179586476925287);
39
40 /** Radians to degrees {@value} */
41 public final static double DR2D = (57.29577951308232087679815);
42
43 /** Degrees to radians {@value}*/
44 public final static double DD2R = (1.745329251994329576923691e-2);
45
46 /** Radians to arcseconds {@value}*/
47 public final static double DR2AS = (206264.8062470963551564734);
48
49 /** Arcseconds to radians {@value}*/
50 public final static double DAS2R = (4.848136811095359935899141e-6);
51
52 /** Arcseconds in a full circle {@value}*/
53 public final static double TURNAS = (1296000.0);
54
55 /** Milliarcseconds to radians {@value}*/
56 public final static double DMAS2R = (DAS2R / 1e3);
57
58 /** Length of tropical year B1900 (days) {@value}*/
59 public final static double DTY = (365.242198781);
60
61 /** Reference epoch (J2000.0), Julian Date {@value}*/
62 public final static double DJ00 = (2451545.0);
63
64 /** Julian Date of Modified Julian Date zero {@value}*/
65 public final static double DJM0 = (2400000.5);
66
67 /** Reference epoch (J2000.0), Modified Julian Date {@value} */
68 public final static double DJM00 = (51544.5);
69
70 /** Seconds per day. {@value}*/
71 public final static double DAYSEC = (86400.0);
72
73 /** Days per Julian year */
74 public final static double DJY = (365.25);
75
76 /** Days per Julian century {@value} */
77 public final static double DJC = (36525.0);
78
79 /** Days per Julian millennium {@value} */
80 public final static double DJM = (365250.0);
81
82 /** 1977 Jan 1.0 as MJD */
83 public final static double DJM77 = (43144.0);
84
85 /** TT minus TAI (s) */
86 public final static double TTMTAI = (32.184);
87
88
89 /** Astronomical unit (m) {@value} */
90 public final static double DAU = (149597870e3);
91
92 /** Speed of light (m/s) */
93 public final static double CMPS = 299792458.0;
94
95 /** Light time for 1 au (s) */
96 public final static double AULT = 499.004782;
97
98
99 /** Speed of light (AU per day) {@value} */
100 public final static double DC = (DAYSEC / AULT);
101
102 /** L_G = 1 - d(TT)/d(TCG) */
103 public final static double ELG = (6.969290134e-10);
104
105 /** L_B = 1 - d(TDB)/d(TCB) at TAI 1977/1/1.0 */
106 public final static double ELB = (1.550519768e-8);
107
108 /** Schwarzschild radius of the Sun (au) {@value}
109 = 2 * 1.32712440041e20 / (2.99792458e8)^2 / 1.49597870700e11 */
110 public final static double SRS = 1.97412574336e-8;
111
112
113 /** TDB (s) at TAI 1977/1/1.0 */
114 public final static double TDB0 = (-6.55e-5);
115
116
117 /** dint(A) - truncate to nearest whole number towards zero (double) */
118 private static double dint(final double A){ return ((A)<0.0?ceil(A):floor(A));}
119
120 /** dnint(A) - round to nearest whole number (double) */
121 private static double dnint(final double A){return ((A)<0.0?ceil((A)-0.5):floor((A)+0.5));}
122
123 /** dsign(A,B) - magnitude of A with sign of B (double) */
124 private static double dsign(final double A, double B){return ((B)<0.0?-abs(A):abs(A));}
125
126
127
128 /**
129 * Julian Date representation. The actual date is djm0+djm1, apportioned in any
130 * convenient way between the two arguments. For example,
131 * JD(TT)=2450123.7 could be expressed in any of these ways,
132 * among others:
133 *<pre>
134 * djm0 djm1
135 *
136 * 2450123.7 0.0 (JD method)
137 * 2451545.0 -1421.3 (J2000 method)
138 * 2400000.5 50123.2 (MJD method)
139 * 2450123.5 0.2 (date &time method)
140 *</pre>
141 *
142 * The JD method is the most natural and convenient to use in
143 * cases where the loss of several decimal digits of resolution
144 * is acceptable. The J2000 method is best matched to the way
145 * the argument is handled internally and will deliver the
146 * optimum resolution. The MJD method and the date &time methods
147 * are both good compromises between resolution and convenience.
148 *
149 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 28 Jan 2010
150 *
151 *
152 */
153 public static class JulianDate {
154 /** MJD zero-point */
155 public double djm0;
156 /** MJD offset */
157 public double djm1;
158 public JulianDate(double d1, double d2) {
159 djm0 = d1;
160 djm1 = d2;
161 }
162 }
163
164 /**
165 * Decompose radians into degrees, arcminutes, arcseconds, fraction.
166 *
167 *
168 * <p>This function is derived from the International Astronomical Union's
169 * SOFA (Standards Of Fundamental Astronomy) software collection.
170 *
171 * <p>Status: vector/matrix support function.
172 *
173 *
174 *
175 *<p>Called:<ul>
176 * <li>{@link #jauD2tf} decompose days to hms
177 *</ul>
178 * <p>Notes:
179 *<ol>
180 * <li> The argument ndp is interpreted as follows:
181 *
182 * <pre>
183 * ndp resolution
184 * : ...0000 00 00
185 * -7 1000 00 00
186 * -6 100 00 00
187 * -5 10 00 00
188 * -4 1 00 00
189 * -3 0 10 00
190 * -2 0 01 00
191 * -1 0 00 10
192 * 0 0 00 01
193 * 1 0 00 00.1
194 * 2 0 00 00.01
195 * 3 0 00 00.001
196 * : 0 00 00.000...
197 *</pre>
198 * <li> The largest positive useful value for ndp is determined by the
199 * size of angle, the format of doubles on the target platform, and
200 * the risk of overflowing idmsf[3]. On a typical platform, for
201 * angle up to 2pi, the available floating-point precision might
202 * correspond to ndp=12. However, the practical limit is typically
203 * ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is
204 * only 16 bits.
205 *
206 * <li> The absolute value of angle may exceed 2pi. In cases where it
207 * does not, it is up to the caller to test for and handle the
208 * case where angle is very nearly 2pi and rounds up to 360 degrees,
209 * by testing for idmsf[0]=360 and setting idmsf[0-3] to zero.
210 *</ol>
211 *@version 2008 May 27
212 *
213 * @since Release 20101201
214 *
215 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
216 * <!-- Given: -->
217 * @param ndp int resolution (Note 1)
218 * @param angle double angle in radians
219 * @param idmsf int[4] <u>returned</u> degrees, arcminutes, arcseconds, fraction
220 * <!-- Returned: -->
221 * @return sign char '+' or '-'
222 */
223 public static char jauA2af(final int ndp, final double angle, int idmsf[] ){
224 /* Hours to degrees * radians to turns */
225 final double F = 15.0 / D2PI;
226
227
228 /* Scale then use days to h,m,s function. */
229 char retval = jauD2tf(ndp, angle*F, idmsf);
230
231 return retval;
232
233
234 }
235
236
237
238 /**
239 * Decompose radians into hours, minutes, seconds, fraction.
240 *
241 *<p>This function is derived from the International Astronomical Union's
242 * SOFA (Standards Of Fundamental Astronomy) software collection.
243 *
244 *<p>Status: vector/matrix support function.
245 *
246 *<!-- Given: -->
247 * @param ndp int resolution (Note 1)
248 * @param angle double angle in radians
249 *
250 *<!-- Returned: -->
251 * @param ihmsf int[4] <u>returned</u> hours, minutes, seconds, fraction
252 * @return sign char <u>returned</u> '+' or '-'
253 *
254 *<p>Called:<ul>
255 * <li>{@link #jauD2tf} decompose days to hms
256 * </ul>
257 * <p>Notes:
258 * <ol>
259 *
260 * <li> The argument ndp is interpreted as follows:
261 * <pre>
262 * ndp resolution
263 * : ...0000 00 00
264 * -7 1000 00 00
265 * -6 100 00 00
266 * -5 10 00 00
267 * -4 1 00 00
268 * -3 0 10 00
269 * -2 0 01 00
270 * -1 0 00 10
271 * 0 0 00 01
272 * 1 0 00 00.1
273 * 2 0 00 00.01
274 * 3 0 00 00.001
275 * : 0 00 00.000...
276 *</pre>
277 * <li> The largest positive useful value for ndp is determined by the
278 * size of angle, the format of doubles on the target platform, and
279 * the risk of overflowing ihmsf[3]. On a typical platform, for
280 * angle up to 2pi, the available floating-point precision might
281 * correspond to ndp=12. However, the practical limit is typically
282 * ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is
283 * only 16 bits.
284 *
285 * <li> The absolute value of angle may exceed 2pi. In cases where it
286 * does not, it is up to the caller to test for and handle the
287 * case where angle is very nearly 2pi and rounds up to 24 hours,
288 * by testing for ihmsf[0]=24 and setting ihmsf(0-3) to zero.
289 *</ol>
290 * @version 2008 May 11
291 *
292 * @since Release 20101201
293 *
294 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
295 */
296 public static char jauA2tf(final int ndp, final double angle, int ihmsf[])
297 {
298 /* Scale then use days to h,m,s function. */
299 return jauD2tf(ndp, angle/D2PI, ihmsf);
300
301 }
302
303
304 /**
305 * Normalize angle into the range {@literal 0 <= a < 2pi}.
306 *
307 *<p>This function is derived from the International Astronomical Union's
308 * SOFA (Standards Of Fundamental Astronomy) software collection.
309 *
310 *<p>Status: vector/matrix support function.
311 *
312 *<!-- Given: -->
313 * @param a double angle (radians)
314 *
315 * <!-- Returned (function value): -->
316 * @return double angle in range 0-2pi
317 *
318 *@version 2008 May 16
319 *
320 * @since Release 20101201
321 *
322 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
323 */
324 public static double jauAnp(final double a)
325 {
326 double w;
327
328
329 w = fmod(a, D2PI);
330 if (w < 0) w += D2PI;
331
332 return w;
333
334 }
335
336
337 /**
338 * Normalize angle into the range {@literal -pi <= a < +pi}.
339 *
340 *<p>This function is derived from the International Astronomical Union's
341 * SOFA (Standards Of Fundamental Astronomy) software collection.
342 *
343 *<p>Status: vector/matrix support function.
344 *
345 *<!-- Given: -->
346 * @param a double angle (radians)
347 *
348 * <!-- Returned (function value): -->
349 * @return double angle in range +/-pi
350 *
351 *@version 2008 May 16
352 *
353 * @since Release 20101201
354 *
355 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
356 */
357 public static double jauAnpm(final double a)
358 {
359 double w;
360
361
362 w = fmod(a, D2PI);
363 if (abs(w) >= DPI) w -= dsign(D2PI, a);
364
365 return w;
366
367 }
368 /**
369 * Frame bias components of IAU 2000 precession-nutation models.
370 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 2 Feb 2010
371 *
372 * @since AIDA Stage 1
373 */
374 public static class FrameBias {
375 /** longitude corrections */
376 public double dpsibi;
377 /**obliquity corrections */
378 public double depsbi;
379 /** the ICRS RA of the J2000.0 mean equinox */
380 public double dra;
381 };
382
383 /**
384 * Frame bias components of IAU 2000 precession-nutation models (part
385 * of MHB2000 with additions).
386 *
387 *<p>This function is derived from the International Astronomical Union's
388 * SOFA (Standards Of Fundamental Astronomy) software collection.
389 *
390 *<p>Status: canonical model.
391 *
392 *<!-- Returned: -->
393 * @return dpsibi,depsbi double <u>returned</u> longitude and obliquity corrections
394 * dra double <u>returned</u> the ICRS RA of the J2000.0 mean equinox
395 *
396 * <p>Notes:
397 * <ol>
398 *
399 * <li> The frame bias corrections in longitude and obliquity (radians)
400 * are required in order to correct for the offset between the GCRS
401 * pole and the mean J2000.0 pole. They define, with respect to the
402 * GCRS frame, a J2000.0 mean pole that is consistent with the rest
403 * of the IAU 2000A precession-nutation model.
404 *
405 * <li> In addition to the displacement of the pole, the complete
406 * description of the frame bias requires also an offset in right
407 * ascension. This is not part of the IAU 2000A model, and is from
408 * Chapront et al. (2002). It is returned in radians.
409 *
410 * <li> This is a supplemented implementation of one aspect of the IAU
411 * 2000A nutation model, formally adopted by the IAU General
412 * Assembly in 2000, namely MHB2000 (Mathews et al. 2002).
413 *</ol>
414 *<p>References:
415 *
416 * Chapront, J., Chapront-Touze, M. &Francou, G., Astron.
417 * Astrophys., 387, 700, 2002.
418 *
419 * <p>Mathews, P.M., Herring, T.A., Buffet, B.A., "Modeling of nutation
420 * and precession New nutation series for nonrigid Earth and
421 * insights into the Earth's interior", J.Geophys.Res., 107, B4,
422 * 2002. The MHB2000 code itself was obtained on 9th September 2002
423 * from ftp://maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
424 *
425 *@version 2009 December 17
426 *
427 * @since Release 20101201
428 *
429 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
430 */
431 public static FrameBias jauBi00()
432 {
433 /* The frame bias corrections in longitude and obliquity */
434 final double DPBIAS = -0.041775 * DAS2R,
435 DEBIAS = -0.0068192 * DAS2R;
436
437 /* The ICRS RA of the J2000.0 equinox (Chapront et al., 2002) */
438 final double DRA0 = -0.0146 * DAS2R;
439
440
441 /* Return the results (which are fixed). */
442 FrameBias retval = new FrameBias();
443 retval.dpsibi = DPBIAS;
444 retval.depsbi = DEBIAS;
445 retval.dra = DRA0;
446
447 return retval;
448
449 }
450
451
452 /**
453 * Frame bias and precession, IAU 2000.
454 *
455 *<p>This function is derived from the International Astronomical Union's
456 * SOFA (Standards Of Fundamental Astronomy) software collection.
457 *
458 *<p>Status: canonical model.
459 *
460 *<!-- Given: -->
461 * @param date1
462 * @param date2 double TT as a 2-part Julian Date (Note 1)
463 *
464 *<!-- Returned: -->
465 * @param rb double[3][3] <u>returned</u> frame bias matrix (Note 2)
466 * @param rp double[3][3] <u>returned</u> precession matrix (Note 3)
467 * @param rbp double[3][3] <u>returned</u> bias-precession matrix (Note 4)
468 *
469 * <p>Notes:
470 * <ol>
471 *
472 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
473 * convenient way between the two arguments. For example,
474 * JD(TT)=2450123.7 could be expressed in any of these ways,
475 * among others:
476 *<pre>
477 * date1 date2
478 *
479 * 2450123.7 0.0 (JD method)
480 * 2451545.0 -1421.3 (J2000 method)
481 * 2400000.5 50123.2 (MJD method)
482 * 2450123.5 0.2 (date &time method)
483 *</pre>
484 * The JD method is the most natural and convenient to use in
485 * cases where the loss of several decimal digits of resolution
486 * is acceptable. The J2000 method is best matched to the way
487 * the argument is handled internally and will deliver the
488 * optimum resolution. The MJD method and the date &time methods
489 * are both good compromises between resolution and convenience.
490 *
491 * <li> The matrix rb transforms vectors from GCRS to mean J2000.0 by
492 * applying frame bias.
493 *
494 * <li> The matrix rp transforms vectors from J2000.0 mean equator and
495 * equinox to mean equator and equinox of date by applying
496 * precession.
497 *
498 * <li> The matrix rbp transforms vectors from GCRS to mean equator and
499 * equinox of date by applying frame bias then precession. It is
500 * the product rp x rb.
501 *
502 * <li> It is permissible to re-use the same array in the returned
503 * arguments. The arrays are filled in the order given.
504 *</ol>
505 *<p>Called:<ul>
506 * <li>{@link #jauBi00} frame bias components, IAU 2000
507 * <li>{@link #jauPr00} IAU 2000 precession adjustments
508 * <li>{@link #jauIr} initialize r-matrix to identity
509 * <li>{@link #jauRx} rotate around X-axis
510 * <li>{@link #jauRy} rotate around Y-axis
511 * <li>{@link #jauRz} rotate around Z-axis
512 * <li>{@link #jauCr} copy r-matrix
513 * <li>{@link #jauRxr} product of two r-matrices
514 * </ul>
515 *<p>Reference:
516 * "Expressions for the Celestial Intermediate Pole and Celestial
517 * Ephemeris Origin consistent with the IAU 2000A precession-
518 * nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
519 *
520 * n.b. The celestial ephemeris origin (CEO) was renamed "celestial
521 * intermediate origin" (CIO) by IAU 2006 Resolution 2.
522 *
523 *@version 2010 January 18
524 *
525 * @since Release 20101201
526 *
527 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
528 */
529 public static void jauBp00(final double date1, final double date2,
530 double rb[][], double rp[][], double rbp[][])
531 {
532 /* J2000.0 obliquity (Lieske et al. 1977) */
533 final double EPS0 = 84381.448 * DAS2R;
534
535 double t, dpsibi, depsbi;
536 double dra0, psia77, oma77, chia, dpsipr, depspr, psia, oma,
537 rbw[][] = new double[3][3];
538
539
540 /* Interval between fundamental epoch J2000.0 and current date (JC). */
541 t = ((date1 - DJ00) + date2) / DJC;
542
543 /* Frame bias. */
544 FrameBias fb = jauBi00();
545 dpsibi = fb.dpsibi;
546 depsbi = fb.depsbi;
547 dra0 = fb.dra;
548 /* Precession angles (Lieske et al. 1977) */
549 psia77 = (5038.7784 + (-1.07259 + (-0.001147) * t) * t) * t * DAS2R;
550 oma77 = EPS0 + ((0.05127 + (-0.007726) * t) * t) * t * DAS2R;
551 chia = ( 10.5526 + (-2.38064 + (-0.001125) * t) * t) * t * DAS2R;
552
553 /* Apply IAU 2000 precession corrections. */
554 PrecessionDeltaTerms pc = jauPr00(date1, date2);
555 dpsipr = pc.dpsipr; depspr = pc.depspr;
556 psia = psia77 + dpsipr;
557 oma = oma77 + depspr;
558
559 /* Frame bias matrix: GCRS to J2000.0. */
560 jauIr(rbw);
561 jauRz(dra0, rbw);
562 jauRy(dpsibi * sin(EPS0), rbw);
563 jauRx(-depsbi, rbw);
564 jauCr(rbw, rb);
565
566 /* Precession matrix: J2000.0 to mean of date. */
567 jauIr(rp);
568 jauRx(EPS0, rp);
569 jauRz(-psia, rp);
570 jauRx(-oma, rp);
571 jauRz(chia, rp);
572
573 /* Bias-precession matrix: GCRS to mean of date. */
574 double[][] rt = jauRxr(rp, rbw );
575 jauCr(rt, rbp);
576 return;
577
578 }
579
580
581 /**
582 * Frame bias and precession, IAU 2006.
583 *
584 *<p>This function is derived from the International Astronomical Union's
585 * SOFA (Standards Of Fundamental Astronomy) software collection.
586 *
587 *<p>Status: support function.
588 *
589 *<!-- Given: -->
590 * @param date1 double TT as a 2-part Julian Date (Note 1)
591 * @param date2 double TT as a 2-part Julian Date (Note 1)
592 *
593 *<!-- Returned: -->
594 * @param rb double[3][3] <u>returned</u> frame bias matrix (Note 2)
595 * @param rp double[3][3] <u>returned</u> precession matrix (Note 3)
596 * @param rbp double[3][3] <u>returned</u> bias-precession matrix (Note 4)
597 *
598 * <p>Notes:
599 * <ol>
600 *
601 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
602 * convenient way between the two arguments. For example,
603 * JD(TT)=2450123.7 could be expressed in any of these ways,
604 * among others:
605 *<pre>
606 * date1 date2
607 *
608 * 2450123.7 0.0 (JD method)
609 * 2451545.0 -1421.3 (J2000 method)
610 * 2400000.5 50123.2 (MJD method)
611 * 2450123.5 0.2 (date &time method)
612 *</pre>
613 * The JD method is the most natural and convenient to use in
614 * cases where the loss of several decimal digits of resolution
615 * is acceptable. The J2000 method is best matched to the way
616 * the argument is handled internally and will deliver the
617 * optimum resolution. The MJD method and the date &time methods
618 * are both good compromises between resolution and convenience.
619 *
620 * <li> The matrix rb transforms vectors from GCRS to mean J2000.0 by
621 * applying frame bias.
622 *
623 * <li> The matrix rp transforms vectors from mean J2000.0 to mean of
624 * date by applying precession.
625 *
626 * <li> The matrix rbp transforms vectors from GCRS to mean of date by
627 * applying frame bias then precession. It is the product rp x rb.
628 *
629 * <li> It is permissible to re-use the same array in the returned
630 * arguments. The arrays are filled in the order given.
631 *</ol>
632 *<p>Called:<ul>
633 * <li>{@link #jauPfw06} bias-precession F-W angles, IAU 2006
634 * <li>{@link #jauFw2m} F-W angles to r-matrix
635 * <li>{@link #jauPmat06} PB matrix, IAU 2006
636 * <li>{@link #jauTr} transpose r-matrix
637 * <li>{@link #jauRxr} product of two r-matrices
638 * </ul>
639 *<p>References:
640 *
641 * <p>Capitaine, N. &Wallace, P.T., 2006, Astron.Astrophys. 450, 855
642 *
643 * <p>Wallace, P.T. &Capitaine, N., 2006, Astron.Astrophys. 459, 981
644 *
645 *@version 2009 December 17
646 *
647 * @since Release 20101201
648 *
649 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
650 */
651 public static void jauBp06(final double date1, final double date2,
652 double rb[][], double rp[][], double rbp[][])
653 {
654 double rbt[][];
655
656
657 /* B matrix. */
658 FWPrecessionAngles fw = jauPfw06(DJM0, DJM00);
659 double[][] rt = jauFw2m(fw.gamb, fw.phib, fw.psib, fw.epsa);
660 jauCr(rt, rb);
661
662 /* PxB matrix. */
663 rt = jauPmat06(date1, date2 );
664 jauCr(rt, rbp);
665
666 /* P matrix. */
667 rbt = jauTr(rb);
668 rt = jauRxr(rbp, rbt);
669 jauCr(rt, rp);
670
671 return;
672
673 }
674
675 /**
676 * The components x,y are components of the Celestial Intermediate
677 * Pole unit vector in the Geocentric Celestial Reference System.
678 *
679 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 29 Jan 2010
680 *
681 * @since AIDA Stage 1
682 */
683 public static class CelestialIntermediatePole {
684 public double x;
685 public double y;
686 public CelestialIntermediatePole(double x, double y) {
687 this.x = x;
688 this.y = y;
689 }
690 }
691 /**
692 * Extract from the bias-precession-nutation matrix the X,Y coordinates
693 * of the Celestial Intermediate Pole.
694 *
695 *<p>This function is derived from the International Astronomical Union's
696 * SOFA (Standards Of Fundamental Astronomy) software collection.
697 *
698 *<p>Status: support function.
699 *
700 *<!-- Given: -->
701 * @param rbpn double[3][3] celestial-to-true matrix (Note 1)
702 *
703 *<!-- Returned: -->
704 * @return <u>returned</u> Celestial Intermediate Pole (Note 2)
705 *
706 * <p>Notes:
707 * <ol>
708 *
709 * <li> The matrix rbpn transforms vectors from GCRS to true equator (and
710 * CIO or equinox) of date, and therefore the Celestial Intermediate
711 * Pole unit vector is the bottom row of the matrix.
712 *
713 * <li> The arguments x,y are components of the Celestial Intermediate
714 * Pole unit vector in the Geocentric Celestial Reference System.
715 *</ol>
716 *<p>Reference:
717 *
718 * "Expressions for the Celestial Intermediate Pole and Celestial
719 * Ephemeris Origin consistent with the IAU 2000A precession-
720 * nutation model", Astron.Astrophys. 400, 1145-1154
721 * (2003)
722 *
723 * n.b. The celestial ephemeris origin (CEO) was renamed "celestial
724 * intermediate origin" (CIO) by IAU 2006 Resolution 2.
725 *
726 *@version 2010 January 18
727 *
728 * @since Release 20101201
729 *
730 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
731 */
732 public static CelestialIntermediatePole jauBpn2xy(double rbpn[][])
733 {
734 /* Extract the X,Y coordinates. */
735
736 return new CelestialIntermediatePole(rbpn[2][0], rbpn[2][1]);
737
738 }
739
740
741 /**
742 * Form the celestial-to-intermediate matrix for a given date using the
743 * IAU 2000A precession-nutation model.
744 *
745 *<p>This function is derived from the International Astronomical Union's
746 * SOFA (Standards Of Fundamental Astronomy) software collection.
747 *
748 *<p>Status: support function.
749 *
750 *<!-- Given: -->
751 * @param date1 double TT as a 2-part Julian Date (Note 1)
752 * @param date2 double TT as a 2-part Julian Date (Note 1)
753 *
754 *<!-- Returned: -->
755 * @return rc2i double[3][3] <u>returned</u> celestial-to-intermediate matrix (Note 2)
756 *
757 * <p>Notes:
758 * <ol>
759 *
760 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
761 * convenient way between the two arguments. For example,
762 * JD(TT)=2450123.7 could be expressed in any of these ways,
763 * among others:
764 *<pre>
765 * date1 date2
766 *
767 * 2450123.7 0.0 (JD method)
768 * 2451545.0 -1421.3 (J2000 method)
769 * 2400000.5 50123.2 (MJD method)
770 * 2450123.5 0.2 (date &time method)
771 *</pre>
772 * The JD method is the most natural and convenient to use in
773 * cases where the loss of several decimal digits of resolution
774 * is acceptable. The J2000 method is best matched to the way
775 * the argument is handled internally and will deliver the
776 * optimum resolution. The MJD method and the date &time methods
777 * are both good compromises between resolution and convenience.
778 *
779 * <li> The matrix rc2i is the first stage in the transformation from
780 * celestial to terrestrial coordinates:
781 *
782 * [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
783 *
784 * = rc2t * [CRS]
785 *
786 * where [CRS] is a vector in the Geocentric Celestial Reference
787 * System and [TRS] is a vector in the International Terrestrial
788 * Reference System (see IERS Conventions 2003), ERA is the Earth
789 * Rotation Angle and RPOM is the polar motion matrix.
790 *
791 * <li> A faster, but slightly less accurate result (about 1 mas), can be
792 * obtained by using instead the jauC2i00b function.
793 *</ol>
794 *<p>Called:<ul>
795 * <li>{@link #jauPnm00a} classical NPB matrix, IAU 2000A
796 * <li>{@link #jauC2ibpn} celestial-to-intermediate matrix, given NPB matrix
797 * </ul>
798 *<p>References:
799 *<ul>
800 * <li>"Expressions for the Celestial Intermediate Pole and Celestial
801 * Ephemeris Origin consistent with the IAU 2000A precession-
802 * nutation model", Astron.Astrophys. 400, 1145-1154
803 * (2003)
804 *
805 * n.b. The celestial ephemeris origin (CEO) was renamed "celestial
806 * intermediate origin" (CIO) by IAU 2006 Resolution 2.
807 *
808 * <li>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
809 * IERS Technical Note No. 32, BKG (2004)
810 *</ul>
811 *@version 2010 January 18
812 *
813 * @since Release 20101201
814 *
815 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
816 */
817 public static double[][] jauC2i00a(double date1, double date2)
818 {
819
820
821 /* Obtain the celestial-to-true matrix (IAU 2000A). */
822 double rbpn[][] = jauPnm00a(date1, date2);
823
824 /* Form the celestial-to-intermediate matrix. */
825 double rc2i[][] =jauC2ibpn(date1, date2, rbpn);
826
827 return rc2i;
828
829 }
830
831
832 /**
833 * Form the celestial-to-intermediate matrix for a given date using the
834 * IAU 2000B precession-nutation model.
835 *
836 *<p>This function is derived from the International Astronomical Union's
837 * SOFA (Standards Of Fundamental Astronomy) software collection.
838 *
839 *<p>Status: support function.
840 *
841 *<!-- Given: -->
842 * @param date1 double TT as a 2-part Julian Date (Note 1)
843 * @param date2 double TT as a 2-part Julian Date (Note 1)
844 *
845 *<!-- Returned: -->
846 * @return rc2i double[3][3] <u>returned</u> celestial-to-intermediate matrix (Note 2)
847 *
848 * <p>Notes:
849 * <ol>
850 *
851 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
852 * convenient way between the two arguments. For example,
853 * JD(TT)=2450123.7 could be expressed in any of these ways,
854 * among others:
855 *<pre>
856 * date1 date2
857 *
858 * 2450123.7 0.0 (JD method)
859 * 2451545.0 -1421.3 (J2000 method)
860 * 2400000.5 50123.2 (MJD method)
861 * 2450123.5 0.2 (date &time method)
862 *</pre>
863 * The JD method is the most natural and convenient to use in
864 * cases where the loss of several decimal digits of resolution
865 * is acceptable. The J2000 method is best matched to the way
866 * the argument is handled internally and will deliver the
867 * optimum resolution. The MJD method and the date &time methods
868 * are both good compromises between resolution and convenience.
869 *
870 * <li> The matrix rc2i is the first stage in the transformation from
871 * celestial to terrestrial coordinates:
872 *
873 * [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
874 *
875 * = rc2t * [CRS]
876 *
877 * where [CRS] is a vector in the Geocentric Celestial Reference
878 * System and [TRS] is a vector in the International Terrestrial
879 * Reference System (see IERS Conventions 2003), ERA is the Earth
880 * Rotation Angle and RPOM is the polar motion matrix.
881 *
882 * <li> The present function is faster, but slightly less accurate (about
883 * 1 mas), than the jauC2i00a function.
884 *</ol>
885 *<p>Called:<ul>
886 * <li>{@link #jauPnm00b} classical NPB matrix, IAU 2000B
887 * <li>{@link #jauC2ibpn} celestial-to-intermediate matrix, given NPB matrix
888 * </ul>
889 *<p>References:
890 *
891 * <p> "Expressions for the Celestial Intermediate Pole and Celestial
892 * Ephemeris Origin consistent with the IAU 2000A precession-
893 * nutation model", Astron.Astrophys. 400, 1145-1154
894 * (2003)
895 *
896 * n.b. The celestial ephemeris origin (CEO) was renamed "celestial
897 * intermediate origin" (CIO) by IAU 2006 Resolution 2.
898 *
899 * <p> McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
900 * IERS Technical Note No. 32, BKG (2004)
901 *
902 *@version 2010 January 18
903 *
904 * @since Release 20101201
905 *
906 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
907 */
908 public static double[][] jauC2i00b(double date1, double date2)
909 {
910 double rbpn[][];
911 double rc2i[][];
912
913 /* Obtain the celestial-to-true matrix (IAU 2000B). */
914 rbpn = jauPnm00b(date1, date2 );
915
916 /* Form the celestial-to-intermediate matrix. */
917 rc2i = jauC2ibpn(date1, date2, rbpn);
918
919 return rc2i;
920
921 }
922
923
924 /**
925 * Form the celestial-to-intermediate matrix for a given date using the
926 * IAU 2006 precession and IAU 2000A nutation models.
927 *
928 *<p>This function is derived from the International Astronomical Union's
929 * SOFA (Standards Of Fundamental Astronomy) software collection.
930 *
931 *<p>Status: support function.
932 *
933 *<!-- Given: -->
934 * @param date1 double TT as a 2-part Julian Date (Note 1)
935 * @param date2 double TT as a 2-part Julian Date (Note 1)
936 *
937 *<!-- Returned: -->
938 * @return rc2i double[3][3] <u>returned</u> celestial-to-intermediate matrix (Note 2)
939 *
940 * <p>Notes:
941 * <ol>
942 *
943 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
944 * convenient way between the two arguments. For example,
945 * JD(TT)=2450123.7 could be expressed in any of these ways,
946 * among others:
947 *<pre>
948 * date1 date2
949 *
950 * 2450123.7 0.0 (JD method)
951 * 2451545.0 -1421.3 (J2000 method)
952 * 2400000.5 50123.2 (MJD method)
953 * 2450123.5 0.2 (date &time method)
954 *</pre>
955 * The JD method is the most natural and convenient to use in
956 * cases where the loss of several decimal digits of resolution
957 * is acceptable. The J2000 method is best matched to the way
958 * the argument is handled internally and will deliver the
959 * optimum resolution. The MJD method and the date &time methods
960 * are both good compromises between resolution and convenience.
961 *
962 * <li> The matrix rc2i is the first stage in the transformation from
963 * celestial to terrestrial coordinates:
964 *
965 * [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
966 *
967 * = RC2T * [CRS]
968 *
969 * where [CRS] is a vector in the Geocentric Celestial Reference
970 * System and [TRS] is a vector in the International Terrestrial
971 * Reference System (see IERS Conventions 2003), ERA is the Earth
972 * Rotation Angle and RPOM is the polar motion matrix.
973 *</ol>
974 *<p>Called:<ul>
975 * <li>{@link #jauPnm06a} classical NPB matrix, IAU 2006/2000A
976 * <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
977 * <li>{@link #jauS06} the CIO locator s, Given X,Y, IAU 2006
978 * <li>{@link #jauC2ixys} celestial-to-intermediate matrix, Given X,Y and s
979 * </ul>
980 *<p>References:
981 *
982 * <p>McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
983 * IERS Technical Note No. 32, BKG
984 *
985 *@version 2008 May 13
986 *
987 * @since Release 20101201
988 *
989 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
990 */
991 public static double[][] jauC2i06a(double date1, double date2)
992 {
993 double rbpn[][], s, rc2i[][];
994
995
996 /* Obtain the celestial-to-true matrix (IAU 2006/2000A). */
997 rbpn = jauPnm06a(date1, date2);
998
999 /* Extract the X,Y coordinates. */
1000 CelestialIntermediatePole cip = jauBpn2xy(rbpn);
1001
1002 /* Obtain the CIO locator. */
1003 s = jauS06(date1, date2, cip.x, cip.y);
1004
1005 /* Form the celestial-to-intermediate matrix. */
1006 rc2i = jauC2ixys(cip.x, cip.y, s);
1007
1008 return rc2i;
1009
1010 }
1011
1012
1013 /**
1014 * Form the celestial-to-intermediate matrix for a given date given
1015 * the bias-precession-nutation matrix. IAU 2000.
1016 *
1017 *<p>This function is derived from the International Astronomical Union's
1018 * SOFA (Standards Of Fundamental Astronomy) software collection.
1019 *
1020 *<p>Status: support function.
1021 *
1022 *<!-- Given: -->
1023 * @param date1 double TT as a 2-part Julian Date (Note 1)
1024 * @param date2 double TT as a 2-part Julian Date (Note 1)
1025 * @param rbpn double[3][3] celestial-to-true matrix (Note 2)
1026 *
1027 *<!-- Returned: -->
1028 * @return rc2i double[3][3] <u>returned</u> celestial-to-intermediate matrix (Note 3)
1029 *
1030 * <p>Notes:
1031 * <ol>
1032 *
1033 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
1034 * convenient way between the two arguments. For example,
1035 * JD(TT)=2450123.7 could be expressed in any of these ways,
1036 * among others:
1037 *<pre>
1038 * date1 date2
1039 *
1040 * 2450123.7 0.0 (JD method)
1041 * 2451545.0 -1421.3 (J2000 method)
1042 * 2400000.5 50123.2 (MJD method)
1043 * 2450123.5 0.2 (date &time method)
1044 *</pre>
1045 * The JD method is the most natural and convenient to use in
1046 * cases where the loss of several decimal digits of resolution
1047 * is acceptable. The J2000 method is best matched to the way
1048 * the argument is handled internally and will deliver the
1049 * optimum resolution. The MJD method and the date &time methods
1050 * are both good compromises between resolution and convenience.
1051 *
1052 * <li> The matrix rbpn transforms vectors from GCRS to true equator (and
1053 * CIO or equinox) of date. Only the CIP (bottom row) is used.
1054 *
1055 * <li> The matrix rc2i is the first stage in the transformation from
1056 * celestial to terrestrial coordinates:
1057 *
1058 * [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
1059 *
1060 * = RC2T * [CRS]
1061 *
1062 * where [CRS] is a vector in the Geocentric Celestial Reference
1063 * System and [TRS] is a vector in the International Terrestrial
1064 * Reference System (see IERS Conventions 2003), ERA is the Earth
1065 * Rotation Angle and RPOM is the polar motion matrix.
1066 *
1067 * <li> Although its name does not include "00", This function is in fact
1068 * specific to the IAU 2000 models.
1069 *</ol>
1070 *<p>Called:<ul>
1071 * <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
1072 * <li>{@link #jauC2ixy} celestial-to-intermediate matrix, given X,Y
1073 * </ul>
1074 *<p>References:
1075 * <p> "Expressions for the Celestial Intermediate Pole and Celestial
1076 * Ephemeris Origin consistent with the IAU 2000A precession-
1077 * nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
1078 *
1079 * <p>n.b. The celestial ephemeris origin (CEO) was renamed "celestial
1080 * intermediate origin" (CIO) by IAU 2006 Resolution 2.
1081 *
1082 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
1083 * IERS Technical Note No. 32, BKG (2004)
1084 *
1085 *@version 2010 January 18
1086 *
1087 * @since Release 20101201
1088 *
1089 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1090 */
1091 public static double[][] jauC2ibpn(double date1, double date2, double rbpn[][])
1092 {
1093
1094 /* Extract the X,Y coordinates. */
1095 CelestialIntermediatePole cip = jauBpn2xy(rbpn);
1096
1097
1098 /* Form the celestial-to-intermediate matrix (n.b. IAU 2000 specific). */
1099 double rc2i[][] =jauC2ixy(date1, date2, cip.x, cip.y);
1100
1101 return rc2i;
1102
1103 }
1104
1105
1106 /**
1107 * Form the celestial to intermediate-frame-of-date matrix for a given
1108 * date when the CIP X,Y coordinates are known. IAU 2000.
1109 *
1110 *<p>This function is derived from the International Astronomical Union's
1111 * SOFA (Standards Of Fundamental Astronomy) software collection.
1112 *
1113 *<p>Status: support function.
1114 *
1115 *<!-- Given: -->
1116 * @param date1 double TT as a 2-part Julian Date (Note 1)
1117 * @param date2 double TT as a 2-part Julian Date (Note 1)
1118 * @param x double Celestial Intermediate Pole (Note 2)
1119 * @param y double Celestial Intermediate Pole (Note 2)
1120 *
1121 *<!-- Returned: -->
1122 * @return rc2i double[3][3] <u>returned</u> celestial-to-intermediate matrix (Note 3)
1123 *
1124 * <p>Notes:
1125 * <ol>
1126 *
1127 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
1128 * convenient way between the two arguments. For example,
1129 * JD(TT)=2450123.7 could be expressed in any of these ways,
1130 * among others:
1131 *<pre>
1132 * date1 date2
1133 *
1134 * 2450123.7 0.0 (JD method)
1135 * 2451545.0 -1421.3 (J2000 method)
1136 * 2400000.5 50123.2 (MJD method)
1137 * 2450123.5 0.2 (date &time method)
1138 *</pre>
1139 * The JD method is the most natural and convenient to use in
1140 * cases where the loss of several decimal digits of resolution
1141 * is acceptable. The J2000 method is best matched to the way
1142 * the argument is handled internally and will deliver the
1143 * optimum resolution. The MJD method and the date &time methods
1144 * are both good compromises between resolution and convenience.
1145 *
1146 * <li> The Celestial Intermediate Pole coordinates are the x,y components
1147 * of the unit vector in the Geocentric Celestial Reference System.
1148 *
1149 * <li> The matrix rc2i is the first stage in the transformation from
1150 * celestial to terrestrial coordinates:
1151 *
1152 * [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
1153 *
1154 * = RC2T * [CRS]
1155 *
1156 * where [CRS] is a vector in the Geocentric Celestial Reference
1157 * System and [TRS] is a vector in the International Terrestrial
1158 * Reference System (see IERS Conventions 2003), ERA is the Earth
1159 * Rotation Angle and RPOM is the polar motion matrix.
1160 *
1161 * <li> Although its name does not include "00", This function is in fact
1162 * specific to the IAU 2000 models.
1163 *</ol>
1164 *<p>Called:<ul>
1165 * <li>{@link #jauC2ixys} celestial-to-intermediate matrix, given X,Y and s
1166 * <li>{@link #jauS00} the CIO locator s, given X,Y, IAU 2000A
1167 * </ul>
1168 *<p>Reference:
1169 *
1170 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
1171 * IERS Technical Note No. 32, BKG (2004)
1172 *
1173 *@version 2008 May 11
1174 *
1175 * @since Release 20101201
1176 *
1177 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1178 */
1179
1180 public static double[][] jauC2ixy(double date1, double date2, double x, double y)
1181 {
1182 /* Compute s and then the matrix. */
1183 double rc2i[][] = jauC2ixys(x, y, jauS00(date1, date2, x, y));
1184
1185 return rc2i;
1186
1187 }
1188
1189
1190 /**
1191 * Form the celestial to intermediate-frame-of-date matrix given the CIP
1192 * X,Y and the CIO locator s.
1193 *
1194 *<p>This function is derived from the International Astronomical Union's
1195 * SOFA (Standards Of Fundamental Astronomy) software collection.
1196 *
1197 *<p>Status: support function.
1198 *
1199 *<!-- Given: -->
1200 * @param x double Celestial Intermediate Pole (Note 1)
1201 * @param y double Celestial Intermediate Pole (Note 1)
1202 * @param s double the CIO locator s (Note 2)
1203 *
1204 *<!-- Returned: -->
1205 * @return rc2i double[3][3] <u>returned</u> celestial-to-intermediate matrix (Note 3)
1206 *
1207 * <p>Notes:
1208 * <ol>
1209 *
1210 * <li> The Celestial Intermediate Pole coordinates are the x,y
1211 * components of the unit vector in the Geocentric Celestial
1212 * Reference System.
1213 *
1214 * <li> The CIO locator s (in radians) positions the Celestial
1215 * Intermediate Origin on the equator of the CIP.
1216 *
1217 * <li> The matrix rc2i is the first stage in the transformation from
1218 * celestial to terrestrial coordinates:
1219 *
1220 * [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
1221 *
1222 * = RC2T * [CRS]
1223 *
1224 * where [CRS] is a vector in the Geocentric Celestial Reference
1225 * System and [TRS] is a vector in the International Terrestrial
1226 * Reference System (see IERS Conventions 2003), ERA is the Earth
1227 * Rotation Angle and RPOM is the polar motion matrix.
1228 *</ol>
1229 *<p>Called:<ul>
1230 * <li>{@link #jauIr} initialize r-matrix to identity
1231 * <li>{@link #jauRz} rotate around Z-axis
1232 * <li>{@link #jauRy} rotate around Y-axis
1233 * </ul>
1234 *<p>Reference:
1235 *
1236 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
1237 * IERS Technical Note No. 32, BKG (2004)
1238 *
1239 *@version 2008 May 11
1240 *
1241 * @since Release 20101201
1242 *
1243 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1244 */
1245 public static double[][] jauC2ixys(double x, double y, double s)
1246 {
1247 double r2, e, d;
1248 double rc2i[][] = new double[3][3];
1249
1250 /* Obtain the spherical angles E and d. */
1251 r2 = x*x + y*y;
1252 e = (r2 > 0.0) ? atan2(y, x) : 0.0;
1253 d = atan(sqrt(r2 / (1.0 - r2)));
1254
1255 /* Form the matrix. */
1256 jauIr(rc2i);
1257 jauRz(e, rc2i);
1258 jauRy(d, rc2i);
1259 jauRz(-(e+s), rc2i);
1260
1261 return rc2i;
1262
1263 }
1264
1265 /**
1266 * P-vector to spherical coordinates.
1267 *
1268 *<p>This function is derived from the International Astronomical Union's
1269 * SOFA (Standards Of Fundamental Astronomy) software collection.
1270 *
1271 *<p>Status: vector/matrix support function.
1272 *
1273 *<!-- Given: -->
1274 * @param p double[3] p-vector
1275 *
1276 *<!-- Returned: -->
1277 * @return theta double <u>returned</u> longitude angle (radians)
1278 * phi double <u>returned</u> latitude angle (radians)
1279 *
1280 * <p>Notes:
1281 * <ol>
1282 *
1283 * <li> The vector p can have any magnitude; only its direction is used.
1284 *
1285 * <li> If p is null, zero theta and phi are returned.
1286 *
1287 * <li> At either pole, zero theta is returned.
1288 *</ol>
1289 *@version 2008 May 11
1290 *
1291 * @since Release 20101201
1292 *
1293 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1294 */
1295 public static SphericalCoordinate jauC2s(double p[])
1296 {
1297 double x, y, z, d2;
1298
1299
1300 x = p[0];
1301 y = p[1];
1302 z = p[2];
1303 d2 = x*x + y*y;
1304
1305 double theta = (d2 == 0.0) ? 0.0 : atan2(y, x);
1306 double phi = (z == 0.0) ? 0.0 : atan2(z, sqrt(d2));
1307
1308 return new SphericalCoordinate(theta, phi);
1309
1310 }
1311
1312
1313 /**
1314 * Form the celestial to terrestrial matrix given the date, the UT1 and
1315 * the polar motion, using the IAU 2000A nutation model.
1316 *
1317 *<p>This function is derived from the International Astronomical Union's
1318 * SOFA (Standards Of Fundamental Astronomy) software collection.
1319 *
1320 *<p>Status: support function.
1321 *
1322 *<!-- Given: -->
1323 * @param tta double TT as a 2-part Julian Date (Note 1)
1324 * @param ttb double TT as a 2-part Julian Date (Note 1)
1325 * @param uta double UT1 as a 2-part Julian Date (Note 1)
1326 * @param utb double UT1 as a 2-part Julian Date (Note 1)
1327 * @param xp double coordinates of the pole (radians, Note 2)
1328 * @param yp double coordinates of the pole (radians, Note 2)
1329 *
1330 *<!-- Returned: -->
1331 * @return rc2t double[3][3] <u>returned</u> celestial-to-terrestrial matrix (Note 3)
1332 *
1333 * <p>Notes:
1334 * <ol>
1335 *
1336 * <li> The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
1337 * apportioned in any convenient way between the arguments uta and
1338 * utb. For example, JD(UT1)=2450123.7 could be expressed in any of
1339 * these ways, among others:
1340 *<pre>
1341 * uta utb
1342 *
1343 * 2450123.7 0.0 (JD method)
1344 * 2451545.0 -1421.3 (J2000 method)
1345 * 2400000.5 50123.2 (MJD method)
1346 * 2450123.5 0.2 (date &time method)
1347 *</pre>
1348 * The JD method is the most natural and convenient to use in
1349 * cases where the loss of several decimal digits of resolution is
1350 * acceptable. The J2000 and MJD methods are good compromises
1351 * between resolution and convenience. In the case of uta,utb, the
1352 * date &time method is best matched to the Earth rotation angle
1353 * algorithm used: maximum precision is delivered when the uta
1354 * argument is for 0hrs UT1 on the day in question and the utb
1355 * argument lies in the range 0 to 1, or vice versa.
1356 *
1357 * <li> The arguments xp and yp are the coordinates (in radians) of the
1358 * Celestial Intermediate Pole with respect to the International
1359 * Terrestrial Reference System (see IERS Conventions 2003),
1360 * measured along the meridians to 0 and 90 deg west respectively.
1361 *
1362 * <li> The matrix rc2t transforms from celestial to terrestrial
1363 * coordinates:
1364 *
1365 * [TRS] = RPOM * R_3(ERA) * RC2I * [CRS]
1366 *
1367 * = rc2t * [CRS]
1368 *
1369 * where [CRS] is a vector in the Geocentric Celestial Reference
1370 * System and [TRS] is a vector in the International Terrestrial
1371 * Reference System (see IERS Conventions 2003), RC2I is the
1372 * celestial-to-intermediate matrix, ERA is the Earth rotation
1373 * angle and RPOM is the polar motion matrix.
1374 *
1375 * <li> A faster, but slightly less accurate result (about 1 mas), can
1376 * be obtained by using instead the jauC2t00b function.
1377 *</ol>
1378 *<p>Called:<ul>
1379 * <li>{@link #jauC2i00a} celestial-to-intermediate matrix, IAU 2000A
1380 * <li>{@link #jauEra00} Earth rotation angle, IAU 2000
1381 * <li>{@link #jauSp00} the TIO locator s', IERS 2000
1382 * <li>{@link #jauPom00} polar motion matrix
1383 * <li>{@link #jauC2tcio} form CIO-based celestial-to-terrestrial matrix
1384 * </ul>
1385 *<p>Reference:
1386 *
1387 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
1388 * IERS Technical Note No. 32, BKG (2004)
1389 *
1390 *@version 2009 April 1
1391 *
1392 * @since Release 20101201
1393 *
1394 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1395 */
1396 public static double[][] jauC2t00a(final double tta, final double ttb, final double uta, final double utb,
1397 final double xp, final double yp)
1398 {
1399 double rc2i[][]= new double[3][3], era, sp, rpom[][];
1400
1401
1402 /* Form the celestial-to-intermediate matrix for this TT (IAU 2000A). */
1403 rc2i = jauC2i00a(tta, ttb);
1404
1405 /* Predict the Earth rotation angle for this UT1. */
1406 era = jauEra00(uta, utb);
1407
1408 /* Estimate s'. */
1409 sp = jauSp00(tta, ttb);
1410
1411 /* Form the polar motion matrix. */
1412 rpom = jauPom00(xp, yp, sp );
1413
1414 /* Combine to form the celestial-to-terrestrial matrix. */
1415 double[][] rc2t = jauC2tcio(rc2i, era, rpom );
1416
1417 return rc2t;
1418
1419 }
1420
1421
1422 /**
1423 * Form the celestial to terrestrial matrix given the date, the UT1 and
1424 * the polar motion, using the IAU 2000B nutation model.
1425 *
1426 *<p>This function is derived from the International Astronomical Union's
1427 * SOFA (Standards Of Fundamental Astronomy) software collection.
1428 *
1429 *<p>Status: support function.
1430 *
1431 *<!-- Given: -->
1432 * @param tta double TT as a 2-part Julian Date (Note 1)
1433 * @param ttb double TT as a 2-part Julian Date (Note 1)
1434 * @param uta double UT1 as a 2-part Julian Date (Note 1)
1435 * @param utb double UT1 as a 2-part Julian Date (Note 1)
1436 * @param xp double coordinates of the pole (radians, Note 2)
1437 * @param yp double coordinates of the pole (radians, Note 2)
1438 *
1439 *<!-- Returned: -->
1440 * @return rc2t double[3][3] <u>returned</u> celestial-to-terrestrial matrix (Note 3)
1441 *
1442 * <p>Notes:
1443 * <ol>
1444 *
1445 * <li> The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
1446 * apportioned in any convenient way between the arguments uta and
1447 * utb. For example, JD(UT1)=2450123.7 could be expressed in any of
1448 * these ways, among others:
1449 *<pre>
1450 * uta utb
1451 *
1452 * 2450123.7 0.0 (JD method)
1453 * 2451545.0 -1421.3 (J2000 method)
1454 * 2400000.5 50123.2 (MJD method)
1455 * 2450123.5 0.2 (date &time method)
1456 *</pre>
1457 * The JD method is the most natural and convenient to use in
1458 * cases where the loss of several decimal digits of resolution is
1459 * acceptable. The J2000 and MJD methods are good compromises
1460 * between resolution and convenience. In the case of uta,utb, the
1461 * date &time method is best matched to the Earth rotation angle
1462 * algorithm used: maximum precision is delivered when the uta
1463 * argument is for 0hrs UT1 on the day in question and the utb
1464 * argument lies in the range 0 to 1, or vice versa.
1465 *
1466 * <li> The arguments xp and yp are the coordinates (in radians) of the
1467 * Celestial Intermediate Pole with respect to the International
1468 * Terrestrial Reference System (see IERS Conventions 2003),
1469 * measured along the meridians to 0 and 90 deg west respectively.
1470 *
1471 * <li> The matrix rc2t transforms from celestial to terrestrial
1472 * coordinates:
1473 *
1474 * [TRS] = RPOM * R_3(ERA) * RC2I * [CRS]
1475 *
1476 * = rc2t * [CRS]
1477 *
1478 * where [CRS] is a vector in the Geocentric Celestial Reference
1479 * System and [TRS] is a vector in the International Terrestrial
1480 * Reference System (see IERS Conventions 2003), RC2I is the
1481 * celestial-to-intermediate matrix, ERA is the Earth rotation
1482 * angle and RPOM is the polar motion matrix.
1483 *
1484 * <li> The present function is faster, but slightly less accurate (about
1485 * 1 mas), than the jauC2t00a function.
1486 *</ol>
1487 *<p>Called:<ul>
1488 * <li>{@link #jauC2i00b} celestial-to-intermediate matrix, IAU 2000B
1489 * <li>{@link #jauEra00} Earth rotation angle, IAU 2000
1490 * <li>{@link #jauPom00} polar motion matrix
1491 * <li>{@link #jauC2tcio} form CIO-based celestial-to-terrestrial matrix
1492 * </ul>
1493 *<p>Reference:
1494 *
1495 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
1496 * IERS Technical Note No. 32, BKG (2004)
1497 *
1498 *@version 2009 April 1
1499 *
1500 * @since Release 20101201
1501 *
1502 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1503 */
1504 public static double[][] jauC2t00b(final double tta, final double ttb, final double uta, final double utb,
1505 final double xp, final double yp )
1506 {
1507 double rc2i[][], era, rpom[][];
1508 double rc2t[][];
1509
1510 /* Form the celestial-to-intermediate matrix for this TT (IAU 2000B). */
1511 rc2i =jauC2i00b(tta, ttb);
1512
1513 /* Predict the Earth rotation angle for this UT1. */
1514 era = jauEra00(uta, utb);
1515
1516 /* Form the polar motion matrix (neglecting s'). */
1517 rpom = jauPom00(xp, yp, 0.0 );
1518
1519 /* Combine to form the celestial-to-terrestrial matrix. */
1520 rc2t = jauC2tcio(rc2i, era, rpom );
1521
1522 return rc2t;
1523
1524 }
1525
1526
1527 /**
1528 * Form the celestial to terrestrial matrix given the date, the UT1 and
1529 * the polar motion, using the IAU 2006 precession and IAU 2000A
1530 * nutation models.
1531 *
1532 *<p>This function is derived from the International Astronomical Union's
1533 * SOFA (Standards Of Fundamental Astronomy) software collection.
1534 *
1535 *<p>Status: support function.
1536 *
1537 *<!-- Given: -->
1538 * @param tta double TT as a 2-part Julian Date (Note 1)
1539 * @param ttb double TT as a 2-part Julian Date (Note 1)
1540 * @param uta double UT1 as a 2-part Julian Date (Note 1)
1541 * @param utb double UT1 as a 2-part Julian Date (Note 1)
1542 * @param xp double coordinates of the pole (radians, Note 2)
1543 * @param yp double coordinates of the pole (radians, Note 2)
1544 *
1545 *<!-- Returned: -->
1546 * @return rc2t double[3][3] <u>returned</u> celestial-to-terrestrial matrix (Note 3)
1547 *
1548 * <p>Notes:
1549 * <ol>
1550 *
1551 * <li> The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
1552 * apportioned in any convenient way between the arguments uta and
1553 * utb. For example, JD(UT1)=2450123.7 could be expressed in any of
1554 * these ways, among others:
1555 *<pre>
1556 * uta utb
1557 *
1558 * 2450123.7 0.0 (JD method)
1559 * 2451545.0 -1421.3 (J2000 method)
1560 * 2400000.5 50123.2 (MJD method)
1561 * 2450123.5 0.2 (date &time method)
1562 *</pre>
1563 * The JD method is the most natural and convenient to use in
1564 * cases where the loss of several decimal digits of resolution is
1565 * acceptable. The J2000 and MJD methods are good compromises
1566 * between resolution and convenience. In the case of uta,utb, the
1567 * date &time method is best matched to the Earth rotation angle
1568 * algorithm used: maximum precision is delivered when the uta
1569 * argument is for 0hrs UT1 on the day in question and the utb
1570 * argument lies in the range 0 to 1, or vice versa.
1571 *
1572 * <li> The arguments xp and yp are the coordinates (in radians) of the
1573 * Celestial Intermediate Pole with respect to the International
1574 * Terrestrial Reference System (see IERS Conventions 2003),
1575 * measured along the meridians to 0 and 90 deg west respectively.
1576 *
1577 * <li> The matrix rc2t transforms from celestial to terrestrial
1578 * coordinates:
1579 *
1580 * [TRS] = RPOM * R_3(ERA) * RC2I * [CRS]
1581 *
1582 * = rc2t * [CRS]
1583 *
1584 * where [CRS] is a vector in the Geocentric Celestial Reference
1585 * System and [TRS] is a vector in the International Terrestrial
1586 * Reference System (see IERS Conventions 2003), RC2I is the
1587 * celestial-to-intermediate matrix, ERA is the Earth rotation
1588 * angle and RPOM is the polar motion matrix.
1589 *</ol>
1590 *<p>Called:<ul>
1591 * <li>{@link #jauC2i06a} celestial-to-intermediate matrix, IAU 2006/2000A
1592 * <li>{@link #jauEra00} Earth rotation angle, IAU 2000
1593 * <li>{@link #jauSp00} the TIO locator s', IERS 2000
1594 * <li>{@link #jauPom00} polar motion matrix
1595 * <li>{@link #jauC2tcio} form CIO-based celestial-to-terrestrial matrix
1596 * </ul>
1597 *<p>Reference:
1598 *
1599 * <p>McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
1600 * IERS Technical Note No. 32, BKG
1601 *
1602 *@version 2009 April 1
1603 *
1604 * @since Release 20101201
1605 *
1606 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1607 */
1608 public static double[][] jauC2t06a(final double tta, final double ttb, final double uta, final double utb,
1609 final double xp, final double yp)
1610 {
1611 double rc2i[][], era, sp, rpom[][], rc2t[][];
1612
1613
1614 /* Form the celestial-to-intermediate matrix for this TT. */
1615 rc2i = jauC2i06a(tta, ttb);
1616
1617 /* Predict the Earth rotation angle for this UT1. */
1618 era = jauEra00(uta, utb);
1619
1620 /* Estimate s'. */
1621 sp = jauSp00(tta, ttb);
1622
1623 /* Form the polar motion matrix. */
1624 rpom = jauPom00(xp, yp, sp );
1625
1626 /* Combine to form the celestial-to-terrestrial matrix. */
1627 rc2t = jauC2tcio(rc2i, era, rpom );
1628
1629 return rc2t;
1630
1631 }
1632
1633
1634 /**
1635 * Assemble the celestial to terrestrial matrix from CIO-based
1636 * components (the celestial-to-intermediate matrix, the Earth Rotation
1637 * Angle and the polar motion matrix).
1638 *
1639 *<p>This function is derived from the International Astronomical Union's
1640 * SOFA (Standards Of Fundamental Astronomy) software collection.
1641 *
1642 *<p>Status: support function.
1643 *
1644 *<!-- Given: -->
1645 * @param rc2i double[3][3] celestial-to-intermediate matrix
1646 * @param era double Earth rotation angle (radians)
1647 * @param rpom double[3][3] polar-motion matrix
1648 *
1649 *<!-- Returned: -->
1650 * @return rc2t double[3][3] <u>returned</u> celestial-to-terrestrial matrix
1651 *
1652 * <p>Notes:
1653 * <ol>
1654 *
1655 * <li> This function constructs the rotation matrix that transforms
1656 * vectors in the celestial system into vectors in the terrestrial
1657 * system. It does so starting from precomputed components, namely
1658 * the matrix which rotates from celestial coordinates to the
1659 * intermediate frame, the Earth rotation angle and the polar motion
1660 * matrix. One use of the present function is when generating a
1661 * series of celestial-to-terrestrial matrices where only the Earth
1662 * Rotation Angle changes, avoiding the considerable overhead of
1663 * recomputing the precession-nutation more often than necessary to
1664 * achieve given accuracy objectives.
1665 *
1666 * <li> The relationship between the arguments is as follows:
1667 *
1668 * [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
1669 *
1670 * = rc2t * [CRS]
1671 *
1672 * where [CRS] is a vector in the Geocentric Celestial Reference
1673 * System and [TRS] is a vector in the International Terrestrial
1674 * Reference System (see IERS Conventions 2003).
1675 *</ol>
1676 *<p>Called:<ul>
1677 * <li>{@link #jauCr} copy r-matrix
1678 * <li>{@link #jauRz} rotate around Z-axis
1679 * <li>{@link #jauRxr} product of two r-matrices
1680 * </ul>
1681 *<p>Reference:
1682 *
1683 * <p>McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
1684 * IERS Technical Note No. 32, BKG
1685 *
1686 *@version 2008 May 11
1687 *
1688 * @since Release 20101201
1689 *
1690 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1691 */
1692 public static double[][] jauC2tcio(final double rc2i[][], final double era, final double rpom[][])
1693 {
1694 double r[][] = new double[3][3];
1695
1696
1697 /* Construct the matrix. */
1698 jauCr(rc2i, r);
1699 jauRz(era, r);
1700 double[][] rc2t = jauRxr(rpom, r);
1701
1702 return rc2t;
1703
1704 }
1705
1706
1707 /**
1708 * Assemble the celestial to terrestrial matrix from equinox-based
1709 * components (the celestial-to-true matrix, the Greenwich Apparent
1710 * Sidereal Time and the polar motion matrix).
1711 *
1712 *<p>This function is derived from the International Astronomical Union's
1713 * SOFA (Standards Of Fundamental Astronomy) software collection.
1714 *
1715 *<p>Status: support function.
1716 *
1717 *<!-- Given: -->
1718 * @param rbpn double[3][3] celestial-to-true matrix
1719 * @param gst double Greenwich (apparent) Sidereal Time (radians)
1720 * @param rpom double[3][3] polar-motion matrix
1721 *
1722 *<!-- Returned: -->
1723 * @return rc2t double[3][3] <u>returned</u> celestial-to-terrestrial matrix (Note 2)
1724 *
1725 * <p>Notes:
1726 * <ol>
1727 *
1728 * <li> This function constructs the rotation matrix that transforms
1729 * vectors in the celestial system into vectors in the terrestrial
1730 * system. It does so starting from precomputed components, namely
1731 * the matrix which rotates from celestial coordinates to the
1732 * true equator and equinox of date, the Greenwich Apparent Sidereal
1733 * Time and the polar motion matrix. One use of the present function
1734 * is when generating a series of celestial-to-terrestrial matrices
1735 * where only the Sidereal Time changes, avoiding the considerable
1736 * overhead of recomputing the precession-nutation more often than
1737 * necessary to achieve given accuracy objectives.
1738 *
1739 * <li> The relationship between the arguments is as follows:
1740 *
1741 * [TRS] = rpom * R_3(gst) * rbpn * [CRS]
1742 *
1743 * = rc2t * [CRS]
1744 *
1745 * where [CRS] is a vector in the Geocentric Celestial Reference
1746 * System and [TRS] is a vector in the International Terrestrial
1747 * Reference System (see IERS Conventions 2003).
1748 *</ol>
1749 *<p>Called:<ul>
1750 * <li>{@link #jauCr} copy r-matrix
1751 * <li>{@link #jauRz} rotate around Z-axis
1752 * <li>{@link #jauRxr} product of two r-matrices
1753 * </ul>
1754 *<p>Reference:
1755 *
1756 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
1757 * IERS Technical Note No. 32, BKG (2004)
1758 *
1759 *@version 2008 May 11
1760 *
1761 * @since Release 20101201
1762 *
1763 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1764 */
1765 public static double[][] jauC2teqx(final double rbpn[][], final double gst, final double rpom[][] )
1766 {
1767 double r[][] = new double[3][3], rc2t[][];
1768
1769
1770 /* Construct the matrix. */
1771 jauCr(rbpn, r);
1772 jauRz(gst, r);
1773 rc2t = jauRxr(rpom, r);
1774
1775 return rc2t;
1776
1777 }
1778
1779
1780 /**
1781 * Form the celestial to terrestrial matrix given the date, the UT1,
1782 * the nutation and the polar motion. IAU 2000.
1783 *
1784 *<p>This function is derived from the International Astronomical Union's
1785 * SOFA (Standards Of Fundamental Astronomy) software collection.
1786 *
1787 *<p>Status: support function.
1788 *
1789 *<!-- Given: -->
1790 * @param tta double TT as a 2-part Julian Date (Note 1)
1791 * @param ttb double TT as a 2-part Julian Date (Note 1)
1792 * @param uta double UT1 as a 2-part Julian Date (Note 1)
1793 * @param utb double UT1 as a 2-part Julian Date (Note 1)
1794 * @param dpsi double nutation (Note 2)
1795 * @param deps double nutation (Note 2)
1796 * @param xp double coordinates of the pole (radians, Note 3)
1797 * @param yp double coordinates of the pole (radians, Note 3)
1798 *
1799 *<!-- Returned: -->
1800 * @return rc2t double[3][3] <u>returned</u> celestial-to-terrestrial matrix (Note 4)
1801 *
1802 * <p>Notes:
1803 * <ol>
1804 *
1805 * <li> The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
1806 * apportioned in any convenient way between the arguments uta and
1807 * utb. For example, JD(UT1)=2450123.7 could be expressed in any of
1808 * these ways, among others:
1809 *<pre>
1810 * uta utb
1811 *
1812 * 2450123.7 0.0 (JD method)
1813 * 2451545.0 -1421.3 (J2000 method)
1814 * 2400000.5 50123.2 (MJD method)
1815 * 2450123.5 0.2 (date &time method)
1816 *</pre>
1817 * The JD method is the most natural and convenient to use in
1818 * cases where the loss of several decimal digits of resolution is
1819 * acceptable. The J2000 and MJD methods are good compromises
1820 * between resolution and convenience. In the case of uta,utb, the
1821 * date &time method is best matched to the Earth rotation angle
1822 * algorithm used: maximum precision is delivered when the uta
1823 * argument is for 0hrs UT1 on the day in question and the utb
1824 * argument lies in the range 0 to 1, or vice versa.
1825 *
1826 * <li> The caller is responsible for providing the nutation components;
1827 * they are in longitude and obliquity, in radians and are with
1828 * respect to the equinox and ecliptic of date. For high-accuracy
1829 * applications, free core nutation should be included as well as
1830 * any other relevant corrections to the position of the CIP.
1831 *
1832 * <li> The arguments xp and yp are the coordinates (in radians) of the
1833 * Celestial Intermediate Pole with respect to the International
1834 * Terrestrial Reference System (see IERS Conventions 2003),
1835 * measured along the meridians to 0 and 90 deg west respectively.
1836 *
1837 * <li> The matrix rc2t transforms from celestial to terrestrial
1838 * coordinates:
1839 *
1840 * [TRS] = RPOM * R_3(GST) * RBPN * [CRS]
1841 *
1842 * = rc2t * [CRS]
1843 *
1844 * where [CRS] is a vector in the Geocentric Celestial Reference
1845 * System and [TRS] is a vector in the International Terrestrial
1846 * Reference System (see IERS Conventions 2003), RBPN is the
1847 * bias-precession-nutation matrix, GST is the Greenwich (apparent)
1848 * Sidereal Time and RPOM is the polar motion matrix.
1849 *
1850 * <li> Although its name does not include "00", This function is in fact
1851 * specific to the IAU 2000 models.
1852 *</ol>
1853 *<p>Called:<ul>
1854 * <li>{@link #jauPn00} bias/precession/nutation results, IAU 2000
1855 * <li>{@link #jauGmst00} Greenwich mean sidereal time, IAU 2000
1856 * <li>{@link #jauSp00} the TIO locator s', IERS 2000
1857 * <li>{@link #jauEe00} equation of the equinoxes, IAU 2000
1858 * <li>{@link #jauPom00} polar motion matrix
1859 * <li>{@link #jauC2teqx} form equinox-based celestial-to-terrestrial matrix
1860 * </ul>
1861 *<p>Reference:
1862 *
1863 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
1864 * IERS Technical Note No. 32, BKG (2004)
1865 *
1866 *@version 2009 April 1
1867 *
1868 * @since Release 20101201
1869 *
1870 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1871 */
1872 public static double[][] jauC2tpe(final double tta, final double ttb, final double uta, final double utb,
1873 final double dpsi, final double deps, final double xp, final double yp)
1874 {
1875 double rpom[][];
1876
1877 /* Form the celestial-to-true matrix for this TT. */
1878 PrecessionNutation pn = jauPn00(tta, ttb, dpsi, deps);
1879
1880 /* Predict the Greenwich Mean Sidereal Time for this UT1 and TT. */
1881 double gmst = jauGmst00(uta, utb, tta, ttb);
1882
1883 /* Predict the equation of the equinoxes given TT and nutation. */
1884 double ee = jauEe00(tta, ttb, pn.epsa, dpsi);
1885
1886 /* Estimate s'. */
1887 double sp = jauSp00(tta, ttb);
1888
1889 /* Form the polar motion matrix. */
1890 rpom = jauPom00(xp, yp, sp);
1891
1892 /* Combine to form the celestial-to-terrestrial matrix. */
1893 double[][] rc2t = jauC2teqx(pn.rbpn, gmst + ee, rpom );
1894
1895 return rc2t;
1896
1897 }
1898
1899
1900 /**
1901 * Form the celestial to terrestrial matrix given the date, the UT1,
1902 * the CIP coordinates and the polar motion. IAU 2000.
1903 *
1904 *<p>This function is derived from the International Astronomical Union's
1905 * SOFA (Standards Of Fundamental Astronomy) software collection.
1906 *
1907 *<p>Status: support function.
1908 *
1909 *<!-- Given: -->
1910 * @param tta double TT as a 2-part Julian Date (Note 1)
1911 * @param ttb double TT as a 2-part Julian Date (Note 1)
1912 * @param uta double UT1 as a 2-part Julian Date (Note 1)
1913 * @param utb double UT1 as a 2-part Julian Date (Note 1)
1914 * @param x double Celestial Intermediate Pole (Note 2)
1915 * @param y double Celestial Intermediate Pole (Note 2)
1916 * @param xp double coordinates of the pole (radians, Note 3)
1917 * @param yp double coordinates of the pole (radians, Note 3)
1918 *
1919 *<!-- Returned: -->
1920 * @return rc2t double[3][3] <u>returned</u> celestial-to-terrestrial matrix (Note 4)
1921 *
1922 * <p>Notes:
1923 * <ol>
1924 *
1925 * <li> The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
1926 * apportioned in any convenient way between the arguments uta and
1927 * utb. For example, JD(UT1)=2450123.7 could be expressed in any o
1928 * these ways, among others:
1929 *<pre>
1930 * uta utb
1931 *
1932 * 2450123.7 0.0 (JD method)
1933 * 2451545.0 -1421.3 (J2000 method)
1934 * 2400000.5 50123.2 (MJD method)
1935 * 2450123.5 0.2 (date &time method)
1936 *</pre>
1937 * The JD method is the most natural and convenient to use in
1938 * cases where the loss of several decimal digits of resolution is
1939 * acceptable. The J2000 and MJD methods are good compromises
1940 * between resolution and convenience. In the case of uta,utb, the
1941 * date &time method is best matched to the Earth rotation angle
1942 * algorithm used: maximum precision is delivered when the uta
1943 * argument is for 0hrs UT1 on the day in question and the utb
1944 * argument lies in the range 0 to 1, or vice versa.
1945 *
1946 * <li> The Celestial Intermediate Pole coordinates are the x,y
1947 * components of the unit vector in the Geocentric Celestial
1948 * Reference System.
1949 *
1950 * <li> The arguments xp and yp are the coordinates (in radians) of the
1951 * Celestial Intermediate Pole with respect to the International
1952 * Terrestrial Reference System (see IERS Conventions 2003),
1953 * measured along the meridians to 0 and 90 deg west respectively.
1954 *
1955 * <li> The matrix rc2t transforms from celestial to terrestrial
1956 * coordinates:
1957 *
1958 * [TRS] = RPOM * R_3(ERA) * RC2I * [CRS]
1959 *
1960 * = rc2t * [CRS]
1961 *
1962 * where [CRS] is a vector in the Geocentric Celestial Reference
1963 * System and [TRS] is a vector in the International Terrestrial
1964 * Reference System (see IERS Conventions 2003), ERA is the Earth
1965 * Rotation Angle and RPOM is the polar motion matrix.
1966 *
1967 * <li> Although its name does not include "00", This function is in fact
1968 * specific to the IAU 2000 models.
1969 *</ol>
1970 *<p>Called:<ul>
1971 * <li>{@link #jauC2ixy} celestial-to-intermediate matrix, given X,Y
1972 * <li>{@link #jauEra00} Earth rotation angle, IAU 2000
1973 * <li>{@link #jauSp00} the TIO locator s', IERS 2000
1974 * <li>{@link #jauPom00} polar motion matrix
1975 * <li>{@link #jauC2tcio} form CIO-based celestial-to-terrestrial matrix
1976 * </ul>
1977 * Reference:
1978 *
1979 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
1980 * IERS Technical Note No. 32, BKG (2004)
1981 *
1982 *@version 2009 April 1
1983 *
1984 * @since Release 20101201
1985 *
1986 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1987 */
1988 public static double[][] jauC2txy(double tta, double ttb, double uta, double utb,
1989 double x, double y, double xp, double yp)
1990 {
1991 double rc2i[][] = new double[3][3], era, sp, rpom[][] = new double[3][3];
1992
1993
1994 /* Form the celestial-to-intermediate matrix for this TT. */
1995 rc2i = jauC2ixy(tta, ttb, x, y);
1996
1997 /* Predict the Earth rotation angle for this UT1. */
1998 era = jauEra00(uta, utb);
1999
2000 /* Estimate s'. */
2001 sp = jauSp00(tta, ttb);
2002
2003 /* Form the polar motion matrix. */
2004 rpom = jauPom00(xp, yp, sp);
2005
2006 /* Combine to form the celestial-to-terrestrial matrix. */
2007 double[][] rc2t = jauC2tcio(rc2i, era, rpom );
2008
2009 return rc2t;
2010
2011 }
2012
2013 /**
2014 * Gregorian Calendar to Julian Date.
2015 *
2016 *<p>This function is derived from the International Astronomical Union's
2017 * SOFA (Standards Of Fundamental Astronomy) software collection.
2018 *
2019 *<p>Status: support function.
2020 *
2021 *<!-- Given: -->
2022 * @param iy,im,id int year, month, day in Gregorian calendar (Note 1)
2023 *
2024 *<!-- Returned: -->
2025 * @return d MJD zero-point: always 2400000.5
2026 * <u>returned</u> Modified Julian Date for 0 hrs
2027 *
2028 * <!-- Returned (function value): -->
2029 * @throws JSOFAIllegalParameter status:
2030 * 0 = OK
2031 * -1 = bad year (Note 3: JD not computed)
2032 * -2 = bad month (JD not computed)
2033 * -3 = bad day (JD computed)
2034 *
2035 * <p>Notes:
2036 * <ol>
2037 *
2038 * <li> The algorithm used is valid from -4800 March 1, but this
2039 * implementation rejects dates before -4799 January 1.
2040 *
2041 * <li> The Julian Date is returned in two pieces, in the usual JSOFA
2042 * manner, which is designed to preserve time resolution. The
2043 * Julian Date is available as a single number by adding djm0 and
2044 * djm.
2045 *
2046 * <li> In early eras the conversion is from the "Proleptic Gregorian
2047 * Calendar"; no account is taken of the date(s) of adoption of
2048 * the Gregorian Calendar, nor is the AD/BC numbering convention
2049 * observed.
2050 *</ol>
2051 *<p>Reference:
2052 *
2053 * <p>Explanatory Supplement to the Astronomical Almanac,
2054 * P. Kenneth Seidelmann (ed), University Science Books (1992),
2055 * Section 12.92 (p604).
2056 *
2057 *@version 2009 October 19
2058 *
2059 * @since Release 20101201
2060 *
2061 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
2062 */
2063 public static JulianDate jauCal2jd(int iy, int im, int id) throws JSOFAIllegalParameter
2064 {
2065 int ly, my;
2066 long iypmy;
2067 double djm0, djm;
2068
2069 /* Earliest year allowed (4800BC) */
2070 final int IYMIN = -4799;
2071
2072 /* Month lengths in days */
2073 final int mtab[]
2074 = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
2075
2076
2077 /* Validate year and month. */
2078 if (iy < IYMIN) throw new JSOFAIllegalParameter("bad year", -1);
2079 if (im < 1 || im > 12) throw new JSOFAIllegalParameter("bad month", -2);
2080
2081 /* If February in a leap year, 1, otherwise 0. */
2082 ly = ((im == 2) &&(iy%4 == 0) && (iy%100 != 0 || (iy%400 == 0)))?1:0;
2083
2084 /* Validate day, taking into account leap years. */
2085 if ( (id < 1) || (id > (mtab[im-1] + ly))) {
2086 }
2087
2088 /* Return result. */
2089 my = (im - 14) / 12;
2090 iypmy = (long) (iy + my);
2091 djm0 = DJM0;
2092 djm = (double)((1461L * (iypmy + 4800L)) / 4L
2093 + (367L * (long) (im - 2 - 12 * my)) / 12L
2094 - (3L * ((iypmy + 4900L) / 100L)) / 4L
2095 + (long) id - 2432076L);
2096
2097 /* Return status. */
2098 return new JulianDate(djm0, djm);
2099
2100 }
2101
2102
2103 /**
2104 * Copy a p-vector.
2105 *
2106 *<p>This function is derived from the International Astronomical Union's
2107 * SOFA (Standards Of Fundamental Astronomy) software collection.
2108 *
2109 *<p>Status: vector/matrix support function.
2110 *
2111 *<!-- Given: -->
2112 * @param p double[3] p-vector to be copied
2113 *
2114 *<!-- Returned: -->
2115 * @param c double[3] <u>given and returned</u> copy
2116 *
2117 *@version 2008 May 11
2118 *
2119 * @since Release 20101201
2120 *
2121 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
2122 */
2123 public static double[] jauCp(double p[], double c[])
2124 {
2125
2126 c[0] = p[0];
2127 c[1] = p[1];
2128 c[2] = p[2];
2129
2130 return c;
2131
2132 }
2133
2134
2135 /**
2136 * Copy a position/velocity vector.
2137 *
2138 *<p>This function is derived from the International Astronomical Union's
2139 * SOFA (Standards Of Fundamental Astronomy) software collection.
2140 *
2141 *<p>Status: vector/matrix support function.
2142 *
2143 *<!-- Given: -->
2144 * @param pv double[2][3] position/velocity vector to be copied
2145 *
2146 *<!-- Returned: -->
2147 * @return c double[2][3] <u>returned</u> copy
2148 *
2149 *<p>Called:<ul>
2150 * <li>{@link #jauCp} copy p-vector
2151 * </ul>
2152 *@version 2008 May 11
2153 *
2154 * @since Release 20101201
2155 *
2156 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
2157 */
2158 public static double[][] jauCpv(double pv[][], double c[][])
2159 {
2160
2161 c[0]=jauCp(pv[0], c[0]);
2162 c[1]=jauCp(pv[1], c[1]);
2163
2164 return c;
2165
2166 }
2167
2168
2169 /**
2170 * Copy an r-matrix.
2171 *
2172 *<p>This function is derived from the International Astronomical Union's
2173 * SOFA (Standards Of Fundamental Astronomy) software collection.
2174 *
2175 *<p>Status: vector/matrix support function.
2176 *
2177 *<!-- Given: -->
2178 * @param r double[3][3] r-matrix to be copied.
2179 *
2180 *<!-- Returned: -->
2181 * @param c double[3][3] <u>given and returned</u> the elements of r are copied into this.
2182 *
2183 *<p>Called:<ul>
2184 * <li>{@link #jauCp} copy p-vector
2185 * </ul>
2186 *@version 2008 May 11
2187 *
2188 * @since Release 20101201
2189 *
2190 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
2191 */
2192 public static void jauCr(double r[][], double c[][] )
2193 {
2194
2195 jauCp(r[0], c[0]);
2196 jauCp(r[1], c[1]);
2197 jauCp(r[2], c[2]);
2198
2199 return;
2200
2201 }
2202
2203
2204 /**
2205 * Decompose days to hours, minutes, seconds, fraction.
2206 *
2207 *<p>This function is derived from the International Astronomical Union's
2208 * SOFA (Standards Of Fundamental Astronomy) software collection.
2209 *
2210 *<p>Status: vector/matrix support function.
2211 *
2212 *<!-- Given: -->
2213 * @param ndp int resolution (Note 1)
2214 * @param days double interval in days
2215 *
2216 *<!-- Returned: -->
2217 * @param ihmsf int[4] <u>returned</u> hours, minutes, seconds, fraction
2218 * @return sign char <u>returned</u> '+' or '-'
2219 *
2220 * <p>Notes:
2221 * <ol>
2222 *
2223 * <li> The argument ndp is interpreted as follows:
2224 *
2225 * ndp resolution
2226 * : ...0000 00 00
2227 * -7 1000 00 00
2228 * -6 100 00 00
2229 * -5 10 00 00
2230 * -4 1 00 00
2231 * -3 0 10 00
2232 * -2 0 01 00
2233 * -1 0 00 10
2234 * 0 0 00 01
2235 * 1 0 00 00.1
2236 * 2 0 00 00.01
2237 * 3 0 00 00.001
2238 * : 0 00 00.000...
2239 *
2240 * <li> The largest positive useful value for ndp is determined by the
2241 * size of days, the format of double on the target platform, and
2242 * the risk of overflowing ihmsf[3]. On a typical platform, for
2243 * days up to 1.0, the available floating-point precision might
2244 * correspond to ndp=12. However, the practical limit is typically
2245 * ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is
2246 * only 16 bits.
2247 *
2248 * <li> The absolute value of days may exceed 1.0. In cases where it
2249 * does not, it is up to the caller to test for and handle the
2250 * case where days is very nearly 1.0 and rounds up to 24 hours,
2251 * by testing for ihms[0]=24 and setting ihmsf[0-3] to zero.
2252 *</ol>
2253 *@version 2008 May 11
2254 *
2255 * @since Release 20101201
2256 *
2257 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
2258 */
2259 public static char jauD2tf(final int ndp, final double days, int ihmsf[])
2260 {
2261 int nrs, n;
2262 double rs, rm, rh, a, w, ah, am, as, af;
2263
2264
2265 /* Handle sign. */
2266 char sign = (char) ( ( days >= 0.0 ) ? '+' : '-' );
2267
2268 /* Interval in seconds. */
2269 a = DAYSEC * abs(days);
2270
2271 /* Pre-round if resolution coarser than 1s (then pretend ndp=1). */
2272 if (ndp < 0) {
2273 nrs = 1;
2274 for (n = 1; n <= -ndp; n++) {
2275 nrs *= (n == 2 || n == 4) ? 6 : 10;
2276 }
2277 rs = (double) nrs;
2278 w = a / rs;
2279 a = rs * dnint(w);
2280 }
2281
2282 /* Express the unit of each field in resolution units. */
2283 nrs = 1;
2284 for (n = 1; n <= ndp; n++) {
2285 nrs *= 10;
2286 }
2287 rs = (double) nrs;
2288 rm = rs * 60.0;
2289 rh = rm * 60.0;
2290
2291 /* Round the interval and express in resolution units. */
2292 a = dnint(rs * a);
2293
2294 /* Break into fields. */
2295 ah = a / rh;
2296 ah = dint(ah);
2297 a -= ah * rh;
2298 am = a / rm;
2299 am = dint(am);
2300 a -= am * rm;
2301 as = a / rs;
2302 as = dint(as);
2303 af = a - as * rs;
2304
2305 /* Return results. */
2306 ihmsf[0] = (int) ah;
2307 ihmsf[1] = (int) am;
2308 ihmsf[2] = (int) as;
2309 ihmsf[3] = (int) af;
2310
2311 return sign;
2312
2313 }
2314
2315 /**
2316 * Representation of Gregorian Calendar with fractional day.
2317 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 4 Feb 2010
2318 *
2319 * @since AIDA Stage 1
2320 */
2321 public static class Calendar {
2322 public final int iy;
2323 public final int im;
2324 public final int id;
2325 public final double fd;
2326 public Calendar (int iy, int im, int id, double fd)
2327 {
2328 this.iy = iy;
2329 this.im = im;
2330 this.id = id;
2331 this.fd = fd;
2332 }
2333 }
2334
2335 /**
2336 * Representation of Gregorian Calendar with integer hours minutes and seconds.
2337 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 4 Feb 2010
2338 *
2339 * @since AIDA Stage 1
2340 */
2341 public static class CalendarHMS {
2342 public final int iy;
2343 public final int im;
2344 public final int id;
2345 public final int ihmsf[];
2346 public CalendarHMS (int iy, int im, int id, int hmsf[]){
2347 this.iy = iy;
2348 this.im = im;
2349 this.id = id;
2350 this.ihmsf = hmsf;
2351 }
2352 }
2353
2354 /**
2355 **
2356 ** Format for output a 2-part Julian Date (or in the case of UTC a
2357 ** quasi-JD form that includes special provision for leap seconds).
2358 **
2359 **<p>This function is derived from the International Astronomical Union's
2360 ** SOFA (Standards of Fundamental Astronomy) software collection.
2361 **
2362 **<p>Status: support function.
2363 **
2364 **<!-- Given: -->
2365 ** scale char[] time scale ID (Note 1)
2366 ** ndp int resolution (Note 2)
2367 ** d1,d2 double time as a 2-part Julian Date (Notes 3,4)
2368 **
2369 **<!-- Returned:-->
2370 ** iy,im,id int year, month, day in Gregorian calendar (Note 5)
2371 ** ihmsf int[4] hours, minutes, seconds, fraction (Note 1)
2372 **
2373 ** Returned (function value):
2374 ** int status: +1 = dubious year (Note 5)
2375 ** 0 = OK
2376 ** -1 = unacceptable date (Note 6)
2377 **
2378 **<p>Notes:
2379 **
2380 ** 1) scale identifies the time scale. Only the value "UTC" (in upper
2381 ** case) is significant, and enables handling of leap seconds (see
2382 ** Note 4).
2383 **
2384 ** 2) ndp is the number of decimal places in the seconds field, and can
2385 ** have negative as well as positive values, such as:
2386 **
2387 ** ndp resolution
2388 ** -4 1 00 00
2389 ** -3 0 10 00
2390 ** -2 0 01 00
2391 ** -1 0 00 10
2392 ** 0 0 00 01
2393 ** 1 0 00 00.1
2394 ** 2 0 00 00.01
2395 ** 3 0 00 00.001
2396 **
2397 ** The limits are platform dependent, but a safe range is -5 to +9.
2398 **
2399 ** 3) d1+d2 is Julian Date, apportioned in any convenient way between
2400 ** the two arguments, for example where d1 is the Julian Day Number
2401 ** and d2 is the fraction of a day. In the case of UTC, where the
2402 ** use of JD is problematical, special conventions apply: see the
2403 ** next note.
2404 **
2405 ** 4) JD cannot unambiguously represent UTC during a leap second unless
2406 ** special measures are taken. The SOFA internal convention is that
2407 ** the quasi-JD day represents UTC days whether the length is 86399,
2408 ** 86400 or 86401 SI seconds. In the 1960-1972 era there were
2409 ** smaller jumps (in either direction) each time the linear UTC(TAI)
2410 ** expression was changed, and these "mini-leaps" are also included
2411 ** in the SOFA convention.
2412 **
2413 ** 5) The warning status "dubious year" flags UTCs that predate the
2414 ** introduction of the time scale or that are too far in the future
2415 ** to be trusted. See iauDat for further details.
2416 **
2417 ** 6) For calendar conventions and limitations, see iauCal2jd.
2418 **
2419 ** Called:
2420 ** iauJd2cal JD to Gregorian calendar
2421 ** iauD2tf decompose days to hms
2422 ** iauDat delta(AT) = TAI-UTC
2423 **
2424 **@version 2014 February 15
2425 **
2426 **@since JSOFA release 20131202
2427 **
2428 ** <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
2429 * @throws JSOFAInternalError
2430 * @throws JSOFAIllegalParameter
2431 */
2432 public static CalendarHMS jauD2dtf(final String scale, int ndp, double d1, double d2 ) throws JSOFAIllegalParameter, JSOFAInternalError
2433 {
2434 boolean leap;
2435 int iy1, im1, id1, iy2, im2, id2, ihmsf1[] = new int[4];
2436 double a1, b1, fd, dat0, dat12, dat24, dleap;
2437
2438
2439 /* The two-part JD. */
2440 a1 = d1;
2441 b1 = d2;
2442
2443 /* Provisional calendar date. */
2444 Calendar cal = jauJd2cal(a1, b1);
2445 iy1 = cal.iy;
2446 im1 = cal.im;
2447 id1 = cal.id;
2448 fd = cal.fd;
2449
2450 /* Is this a leap second day? */
2451 leap = false;
2452 if ( scale.equalsIgnoreCase("UTC") ) {
2453
2454 /* TAI-UTC at 0h today. */
2455 dat0 = jauDat(iy1, im1, id1, 0.0 );
2456
2457 /* TAI-UTC at 12h today (to detect drift). */
2458 dat12 = jauDat(iy1, im1, id1, 0.5);
2459
2460 /* TAI-UTC at 0h tomorrow (to detect jumps). */
2461 cal = jauJd2cal(a1+1.5, b1-fd);
2462 iy2 = cal.iy;
2463 im2 = cal.im;
2464 id2 = cal.id;
2465 dat24 = jauDat(iy2, im2, id2, 0.0);
2466
2467 /* Any sudden change in TAI-UTC (seconds). */
2468 dleap = dat24 - (2.0*dat12 - dat0);
2469
2470 /* If leap second day, scale the fraction of a day into SI. */
2471 leap = (dleap != 0.0);
2472 if (leap) fd += fd * dleap/DAYSEC;
2473 }
2474
2475 jauD2tf ( ndp, fd, ihmsf1 );
2476
2477 /* Has the (rounded) time gone past 24h? */
2478 if ( ihmsf1[0] > 23 ) {
2479
2480 /* Yes. We probably need tomorrow's calendar date. */
2481 cal = jauJd2cal(a1+1.5, b1-fd);
2482 iy2 = cal.iy; im2 = cal.im; id2 = cal.id;
2483
2484 /* Is today a leap second day? */
2485 if ( ! leap ) {
2486
2487 /* No. Use 0h tomorrow. */
2488 iy1 = iy2;
2489 im1 = im2;
2490 id1 = id2;
2491 ihmsf1[0] = 0;
2492 ihmsf1[1] = 0;
2493 ihmsf1[2] = 0;
2494
2495 } else {
2496
2497 /* Yes. Are we past the leap second itself? */
2498 if ( ihmsf1[2] > 0 ) {
2499
2500 /* Yes. Use tomorrow but allow for the leap second. */
2501 iy1 = iy2;
2502 im1 = im2;
2503 id1 = id2;
2504 ihmsf1[0] = 0;
2505 ihmsf1[1] = 0;
2506 ihmsf1[2] = 0;
2507
2508 } else {
2509
2510 /* No. Use 23 59 60... today. */
2511 ihmsf1[0] = 23;
2512 ihmsf1[1] = 59;
2513 ihmsf1[2] = 60;
2514 }
2515
2516 /* If rounding to 10s or coarser always go up to new day. */
2517 if ( ndp < 0 && ihmsf1[2] == 60 ) {
2518 iy1 = iy2;
2519 im1 = im2;
2520 id1 = id2;
2521 ihmsf1[0] = 0;
2522 ihmsf1[1] = 0;
2523 ihmsf1[2] = 0;
2524 }
2525 }
2526 }
2527
2528 /* Results. */
2529
2530 return new CalendarHMS(iy1, im1, id1, ihmsf1);
2531
2532 }
2533
2534 /**
2535 ** Encode date and time fields into 2-part Julian Date (or in the case
2536 ** of UTC a quasi-JD form that includes special provision for leap
2537 ** seconds).
2538 **
2539 **<p>This function is derived from the International Astronomical Union's
2540 ** SOFA (Standards of Fundamental Astronomy) software collection.
2541 **
2542 ** Status: support function.
2543 **
2544 ** Given:
2545 ** @param scale char time scale ID (Note 1)
2546 ** @param iy,im,id int year, month, day in Gregorian calendar (Note 2)
2547 ** @param ihr,imn int hour, minute
2548 ** @param sec double seconds
2549 **
2550 ** Returned:
2551 ** @return 2-part Julian Date (Notes 3,4)
2552 **
2553 * @throws JSOFAIllegalParameter
2554 * @throws JSOFAInternalError
2555 ** {@literal status: +3 = both of next two
2556 ** +2 = time is after end of day (Note 5)
2557 ** +1 = dubious year (Note 6)
2558 ** 0 = OK
2559 ** -1 = bad year
2560 ** -2 = bad month
2561 ** -3 = bad day
2562 ** -4 = bad hour
2563 ** -5 = bad minute
2564 ** -6 = bad second (<0)}
2565 **
2566 **<p>Notes:
2567 **
2568 ** 1) scale identifies the time scale. Only the value "UTC" (in upper
2569 ** case) is significant, and enables handling of leap seconds (see
2570 ** Note 4).
2571 **
2572 ** 2) For calendar conventions and limitations, see iauCal2jd.
2573 **
2574 ** 3) The sum of the results, d1+d2, is Julian Date, where normally d1
2575 ** is the Julian Day Number and d2 is the fraction of a day. In the
2576 ** case of UTC, where the use of JD is problematical, special
2577 ** conventions apply: see the next note.
2578 **
2579 ** 4) JD cannot unambiguously represent UTC during a leap second unless
2580 ** special measures are taken. The SOFA internal convention is that
2581 ** the quasi-JD day represents UTC days whether the length is 86399,
2582 ** 86400 or 86401 SI seconds. In the 1960-1972 era there were
2583 ** smaller jumps (in either direction) each time the linear UTC(TAI)
2584 ** expression was changed, and these "mini-leaps" are also included
2585 ** in the SOFA convention.
2586 **
2587 ** 5) The warning status "time is after end of day" usually means that
2588 ** the sec argument is greater than 60.0. However, in a day ending
2589 ** in a leap second the limit changes to 61.0 (or 59.0 in the case
2590 ** of a negative leap second).
2591 **
2592 ** 6) The warning status "dubious year" flags UTCs that predate the
2593 ** introduction of the time scale or that are too far in the future
2594 ** to be trusted. See iauDat for further details.
2595 **
2596 ** 7) Only in the case of continuous and regular time scales (TAI, TT,
2597 ** TCG, TCB and TDB) is the result d1+d2 a Julian Date, strictly
2598 ** speaking. In the other cases (UT1 and UTC) the result must be
2599 ** used with circumspection; in particular the difference between
2600 ** two such results cannot be interpreted as a precise time
2601 ** interval.
2602 **
2603 ** Called:
2604 ** iauCal2jd Gregorian calendar to JD
2605 ** iauDat delta(AT) = TAI-UTC
2606 ** iauJd2cal JD to Gregorian calendar
2607 **
2608 **@version 2013 July 26
2609 **
2610 **@since JSOFA release 20131202
2611 **
2612 ** <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
2613 */
2614 public static JulianDate jauDtf2d(final String scale, int iy, int im, int id,
2615 int ihr, int imn, double sec) throws JSOFAIllegalParameter, JSOFAInternalError
2616 {
2617 int js = 0, iy2, im2, id2;
2618 double dj, w, day, seclim, dat0, dat12, dat24, dleap, time;
2619
2620
2621 /* Today's Julian Day Number. */
2622 JulianDate jd = jauCal2jd(iy, im, id);
2623 dj = jd.djm0; w = jd.djm1;
2624 dj += w;
2625
2626 /* Day length and final minute length in seconds (provisional). */
2627 day = DAYSEC;
2628 seclim = 60.0;
2629
2630 /* Deal with the UTC leap second case. */
2631 if ( scale.equals("UTC") ) {
2632
2633 /* TAI-UTC at 0h today. */
2634 dat0 = jauDat(iy, im, id, 0.0);
2635
2636 /* TAI-UTC at 12h today (to detect drift). */
2637 dat12 = jauDat(iy, im, id, 0.5);
2638
2639 /* TAI-UTC at 0h tomorrow (to detect jumps). */
2640 Calendar cal = jauJd2cal ( dj, 1.5);
2641 iy2 = cal.iy; im2 = cal.im; id2 = cal.id; w = cal.fd;
2642
2643 dat24 = jauDat(iy2, im2, id2, 0.0);
2644
2645 /* Any sudden change in TAI-UTC between today and tomorrow. */
2646 dleap = dat24 - (2.0*dat12 - dat0);
2647
2648 /* If leap second day, correct the day and final minute lengths. */
2649 day += dleap;
2650 if ( ihr == 23 && imn == 59 ) seclim += dleap;
2651
2652 /* End of UTC-specific actions. */
2653 }
2654
2655 /* Validate the time. */
2656 if ( ihr >= 0 && ihr <= 23 ) {
2657 if ( imn >= 0 && imn <= 59 ) {
2658 if ( sec >= 0 ) {
2659 if ( sec >= seclim ) {
2660 js += 2;
2661 }
2662 } else {
2663 js = -6;
2664 }
2665 } else {
2666 js = -5;
2667 }
2668 } else {
2669 js = -4;
2670 }
2671 if ( js < 0 ) throw new JSOFAInternalError("problem with time", js);
2672
2673 /* The time in days. */
2674 time = ( 60.0 * ( (double) ( 60 * ihr + imn ) ) + sec ) / day;
2675
2676 /* Return the date and time. */
2677 return new JulianDate(dj, time) ;
2678
2679 }
2680
2681
2682
2683 /** Release year for this version of jauDat {@value} */
2684 public final static int IYV = 2016;
2685 static class LeapInfo {
2686 final public int iyear, month;
2687 final public double delat;
2688 public LeapInfo(int i, int m, double t) {
2689 iyear = i;
2690 month = m;
2691 delat = t;
2692 }
2693 }
2694
2695 /* Dates and Delta(AT)s */
2696 static final LeapInfo leapSeconds[] = {
2697 new LeapInfo( 1960, 1, 1.4178180 ),
2698 new LeapInfo( 1961, 1, 1.4228180 ),
2699 new LeapInfo( 1961, 8, 1.3728180 ),
2700 new LeapInfo( 1962, 1, 1.8458580 ),
2701 new LeapInfo( 1963, 11, 1.9458580 ),
2702 new LeapInfo( 1964, 1, 3.2401300 ),
2703 new LeapInfo( 1964, 4, 3.3401300 ),
2704 new LeapInfo( 1964, 9, 3.4401300 ),
2705 new LeapInfo( 1965, 1, 3.5401300 ),
2706 new LeapInfo( 1965, 3, 3.6401300 ),
2707 new LeapInfo( 1965, 7, 3.7401300 ),
2708 new LeapInfo( 1965, 9, 3.8401300 ),
2709 new LeapInfo( 1966, 1, 4.3131700 ),
2710 new LeapInfo( 1968, 2, 4.2131700 ),
2711 new LeapInfo( 1972, 1, 10.0 ),
2712 new LeapInfo( 1972, 7, 11.0 ),
2713 new LeapInfo( 1973, 1, 12.0 ),
2714 new LeapInfo( 1974, 1, 13.0 ),
2715 new LeapInfo( 1975, 1, 14.0 ),
2716 new LeapInfo( 1976, 1, 15.0 ),
2717 new LeapInfo( 1977, 1, 16.0 ),
2718 new LeapInfo( 1978, 1, 17.0 ),
2719 new LeapInfo( 1979, 1, 18.0 ),
2720 new LeapInfo( 1980, 1, 19.0 ),
2721 new LeapInfo( 1981, 7, 20.0 ),
2722 new LeapInfo( 1982, 7, 21.0 ),
2723 new LeapInfo( 1983, 7, 22.0 ),
2724 new LeapInfo( 1985, 7, 23.0 ),
2725 new LeapInfo( 1988, 1, 24.0 ),
2726 new LeapInfo( 1990, 1, 25.0 ),
2727 new LeapInfo( 1991, 1, 26.0 ),
2728 new LeapInfo( 1992, 7, 27.0 ),
2729 new LeapInfo( 1993, 7, 28.0 ),
2730 new LeapInfo( 1994, 7, 29.0 ),
2731 new LeapInfo( 1996, 1, 30.0 ),
2732 new LeapInfo( 1997, 7, 31.0 ),
2733 new LeapInfo( 1999, 1, 32.0 ),
2734 new LeapInfo( 2006, 1, 33.0 ),
2735 new LeapInfo( 2009, 1, 34.0 ),
2736 new LeapInfo( 2012, 7, 35.0 ),
2737 new LeapInfo( 2015, 7, 36.0 ),
2738 new LeapInfo( 2017, 1, 37.0 )
2739 };
2740
2741 /**
2742 * For a given UTC date, calculate delta(AT) = TAI-UTC.
2743 *<pre>
2744 * :------------------------------------------:
2745 * : :
2746 * : IMPORTANT :
2747 * : :
2748 * : A new version of this function must be :
2749 * : produced whenever a new leap second is :
2750 * : announced. There are four items to :
2751 * : change on each such occasion: :
2752 * : :
2753 * : 1) A new line must be added to the set :
2754 * : of statements that initialize the :
2755 * : array "changes". :
2756 * : :
2757 * : 2) The parameter IYV must be set to :
2758 * : the current year. :
2759 * : :
2760 * : 3) The "Latest leap second" comment :
2761 * : below must be set to the new leap :
2762 * : second date. :
2763 * : :
2764 * : 4) The "This revision" comment, later, :
2765 * : must be set to the current date. :
2766 * : :
2767 * : Change (2) must also be carried out :
2768 * : whenever the function is re-issued, :
2769 * : even if no leap seconds have been :
2770 * : added. :
2771 * : :
2772 * : Latest leap second: 2017 Jan 01 :
2773 * : :
2774 * :__________________________________________:
2775 *</pre>
2776 *<p>This function is derived from the International Astronomical Union's
2777 * SOFA (Standards Of Fundamental Astronomy) software collection.
2778 *
2779 *<p>Status: support function.
2780 *
2781 *<!-- Given: -->
2782 * @param iy int UTC: year (Notes 1 and 2)
2783 * @param im int month (Note 2)
2784 * @param id int day (Notes 2 and 3)
2785 * @param fd double fraction of day (Note 4)
2786 *
2787 *<!-- Returned: -->
2788 * @return deltat double <u>returned</u> TAI minus UTC, seconds
2789 *
2790 * @throws JSOFAIllegalParameter status (Note 5):
2791 * 1 = dubious year (Note 1)
2792 * 0 = OK
2793 * -1 = bad year
2794 * -2 = bad month
2795 * -3 = bad day (Note 3)
2796 * -4 = bad fraction (Note 4)
2797 *
2798 * <p>Notes:
2799 * <ol>
2800 *
2801 * <li> UTC began at 1960 January 1.0 (JD 2436934.5) and it is improper
2802 * to call the function with an earlier date. If this is attempted,
2803 * zero is returned together with a warning status.
2804 *
2805 * Because leap seconds cannot, in principle, be predicted in
2806 * advance, a reliable check for dates beyond the valid range is
2807 * impossible. To guard against gross errors, a year five or more
2808 * after the release year of the present function (see parameter
2809 * IYV) is considered dubious. In this case a warning status is
2810 * returned but the result is computed in the normal way.
2811 *
2812 * For both too-early and too-late years, the warning status is
2813 * j=+1. This is distinct from the error status j=-1, which
2814 * signifies a year so early that JD could not be computed.
2815 *
2816 * <li> If the specified date is for a day which ends with a leap second,
2817 * the UTC-TAI value returned is for the period leading up to the
2818 * leap second. If the date is for a day which begins as a leap
2819 * second ends, the UTC-TAI returned is for the period following the
2820 * leap second.
2821 *
2822 * <li> The day number must be in the normal calendar range, for example
2823 * 1 through 30 for April. The "almanac" convention of allowing
2824 * such dates as January 0 and December 32 is not supported in this
2825 * function, in order to avoid confusion near leap seconds.
2826 *
2827 * <li> The fraction of day is used only for dates before the
2828 * introduction of leap seconds, the first of which occurred at the
2829 * end of 1971. It is tested for validity (zero to less than 1 is
2830 * the valid range) even if not used; if invalid, zero is used and
2831 * status j=-4 is returned. For many applications, setting fd to
2832 * zero is acceptable; the resulting error is always less than 3 ms
2833 * (and occurs only pre-1972).
2834 *
2835 * <li> The status value returned in the case where there are multiple
2836 * errors refers to the first error detected. For example, if the
2837 * month and day are 13 and 32 respectively, j=-2 (bad month)
2838 * will be returned.
2839 *
2840 * <li> In cases where a valid result is not available, zero is returned.
2841 *
2842 *<p>References:
2843 *
2844 * <li> For dates from 1961 January 1 onwards, the expressions from the
2845 * file ftp://maia.usno.navy.mil/ser7/tai-utc.dat are used.
2846 *
2847 * <li> The 5ms timestep at 1961 January 1 is taken from 2.58.1 (p87) of
2848 * the 1992 Explanatory Supplement.
2849 *</ol>
2850 *<p>Called:<ul>
2851 * <li>{@link #jauCal2jd} Gregorian calendar to Julian Day number
2852 * </ul>
2853 *<p>@version 20160729
2854 *
2855 * @since Release 20101201
2856 *
2857 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
2858 */
2859 public static double jauDat(int iy, int im, int id, double fd ) throws JSOFAIllegalParameter, JSOFAInternalError
2860 {
2861
2862 /* Reference dates (MJD) and drift rates (s/day), pre leap seconds */
2863 final double drift[][] = {
2864 { 37300.0, 0.0012960 },
2865 { 37300.0, 0.0012960 },
2866 { 37300.0, 0.0012960 },
2867 { 37665.0, 0.0011232 },
2868 { 37665.0, 0.0011232 },
2869 { 38761.0, 0.0012960 },
2870 { 38761.0, 0.0012960 },
2871 { 38761.0, 0.0012960 },
2872 { 38761.0, 0.0012960 },
2873 { 38761.0, 0.0012960 },
2874 { 38761.0, 0.0012960 },
2875 { 38761.0, 0.0012960 },
2876 { 39126.0, 0.0025920 },
2877 { 39126.0, 0.0025920 }
2878 };
2879
2880 /* Number of Delta(AT) expressions before leap seconds were introduced */
2881 final int NERA1 = drift.length;
2882
2883
2884 /* Number of Delta(AT) changes */
2885 final int NDAT = leapSeconds.length;
2886
2887 /* Miscellaneous local variables */
2888 int i, m;
2889 double da, djm;
2890
2891
2892 /* Initialize the result to zero. */
2893 double deltat = da = 0.0;
2894
2895 /* If invalid fraction of a day, set error status and give up. */
2896 if (fd < 0.0 || fd > 1.0) throw new JSOFAIllegalParameter("bad day fraction", -4);
2897
2898 /* Convert the date into an MJD. */
2899 JulianDate jd = jauCal2jd(iy, im, id);
2900 djm = jd.djm1;
2901
2902 /* If pre-UTC year, set warning status and give up. */
2903 if (iy < leapSeconds[0].iyear) throw new JSOFAInternalError("year before UTC start", 1);
2904
2905 /* If suspiciously late year, set warning status but proceed. */
2906 if (iy > IYV + 5) {
2907 }
2908
2909 /* Combine year and month to form a date-ordered integer... */
2910 m = 12*iy + im;
2911
2912 /* ...and use it to find the preceding table entry. */
2913 for (i = NDAT-1; i >=0; i--) {
2914 if (m >= (12 * leapSeconds[i].iyear + leapSeconds[i].month)) break;
2915 }
2916
2917 /* Get the Delta(AT). */
2918 da = leapSeconds[i].delat;
2919
2920 /* If pre-1972, adjust for drift. */
2921 if (i < NERA1) da += (djm + fd - drift[i][0]) * drift[i][1];
2922
2923 /* Return the Delta(AT) value. */
2924 deltat = da;
2925
2926 /* Return the value. */
2927 return deltat;
2928
2929 }
2930
2931
2932 /**
2933 * An approximation to TDB-TT, the difference between barycentric
2934 * dynamical time and terrestrial time, for an observer on the Earth.
2935 *
2936 * The different time scales - proper, coordinate and realized - are
2937 * related to each other:
2938 * {@code
2939 * TAI <- physically realized
2940 * :
2941 * offset <- observed (nominally +32.184s)
2942 * :
2943 * TT <- terrestrial time
2944 * :
2945 * rate adjustment (L_G) <- definition of TT
2946 * :
2947 * TCG <- time scale for GCRS
2948 * :
2949 * "periodic" terms <- jauDtdb is an implementation
2950 * :
2951 * rate adjustment (L_C) <- function of solar-system ephemeris
2952 * :
2953 * TCB <- time scale for BCRS
2954 * :
2955 * rate adjustment (-L_B) <- definition of TDB
2956 * :
2957 * TDB <- TCB scaled to track TT
2958 * :
2959 * "periodic" terms <- -jau_DTDB is an approximation
2960 * :
2961 * TT <- terrestrial time
2962 *}
2963 * Adopted values for the various constants can be found in the IERS
2964 * Conventions (McCarthy & Petit 2003).
2965 *
2966 *<p>This function is derived from the International Astronomical Union's
2967 * SOFA (Standards Of Fundamental Astronomy) software collection.
2968 *
2969 *<p>Status: canonical model.
2970 *
2971 *<!-- Given: -->
2972 * @param date1 double date, TDB (Notes 1-3)
2973 * @param date2 double date, TDB (Notes 1-3)
2974 * @param ut double universal time (UT1, fraction of one day)
2975 * @param elong double longitude (east positive, radians)
2976 * @param u double distance from Earth spin axis (km)
2977 * @param v double distance north of equatorial plane (km)
2978 *
2979 * <!-- Returned (function value): -->
2980 * @return @return double TDB-TT (seconds)
2981 *
2982 * <p>Notes:
2983 * <ol>
2984 *
2985 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
2986 * convenient way between the two arguments. For example,
2987 * JD(TT)=2450123.7 could be expressed in any of these ways,
2988 * among others:
2989 *<pre>
2990 * date1 date2
2991 *
2992 * 2450123.7 0.0 (JD method)
2993 * 2451545.0 -1421.3 (J2000 method)
2994 * 2400000.5 50123.2 (MJD method)
2995 * 2450123.5 0.2 (date & time method)
2996 *</pre>
2997 * The JD method is the most natural and convenient to use in
2998 * cases where the loss of several decimal digits of resolution
2999 * is acceptable. The J2000 method is best matched to the way
3000 * the argument is handled internally and will deliver the
3001 * optimum resolution. The MJD method and the date & time methods
3002 * are both good compromises between resolution and convenience.
3003 *
3004 * Although the date is, formally, barycentric dynamical time (TDB),
3005 * the terrestrial dynamical time (TT) can be used with no practical
3006 * effect on the accuracy of the prediction.
3007 *
3008 * <li> TT can be regarded as a coordinate time that is realized as an
3009 * offset of 32.184s from International Atomic Time, TAI. TT is a
3010 * specific linear transformation of geocentric coordinate time TCG,
3011 * which is the time scale for the Geocentric Celestial Reference
3012 * System, GCRS.
3013 *
3014 * <li> TDB is a coordinate time, and is a specific linear transformation
3015 * of barycentric coordinate time TCB, which is the time scale for
3016 * the Barycentric Celestial Reference System, BCRS.
3017 *
3018 * <li> The difference TCG-TCB depends on the masses and positions of the
3019 * bodies of the solar system and the velocity of the Earth. It is
3020 * dominated by a rate difference, the residual being of a periodic
3021 * character. The latter, which is modeled by the present function,
3022 * comprises a main (annual) sinusoidal term of amplitude
3023 * approximately 0.00166 seconds, plus planetary terms up to about
3024 * 20 microseconds, and lunar and diurnal terms up to 2 microseconds.
3025 * These effects come from the changing transverse Doppler effect
3026 * and gravitational red-shift as the observer (on the Earth's
3027 * surface) experiences variations in speed (with respect to the
3028 * BCRS) and gravitational potential.
3029 *
3030 * <li> TDB can be regarded as the same as TCB but with a rate adjustment
3031 * to keep it close to TT, which is convenient for many applications.
3032 * The history of successive attempts to define TDB is set out in
3033 * Resolution 3 adopted by the IAU General Assembly in 2006, which
3034 * defines a fixed TDB(TCB) transformation that is consistent with
3035 * contemporary solar-system ephemerides. Future ephemerides will
3036 * imply slightly changed transformations between TCG and TCB, which
3037 * could introduce a linear drift between TDB and TT; however, any
3038 * such drift is unlikely to exceed 1 nanosecond per century.
3039 *
3040 * <li> The geocentric TDB-TT model used in the present function is that of
3041 * Fairhead & Bretagnon (1990), in its full form. It was originally
3042 * supplied by Fairhead (private communications with P.T.Wallace,
3043 * 1990) as a Fortran subroutine. The present C function contains an
3044 * adaptation of the Fairhead code. The numerical results are
3045 * essentially unaffected by the changes, the differences with
3046 * respect to the Fairhead & Bretagnon original being at the 1e-20 s
3047 * level.
3048 *
3049 * The topocentric part of the model is from Moyer (1981) and
3050 * Murray (1983), with fundamental arguments adapted from
3051 * Simon et al. 1994. It is an approximation to the expression
3052 * ( v / c ) . ( r / c ), where v is the barycentric velocity of
3053 * the Earth, r is the geocentric position of the observer and
3054 * c is the speed of light.
3055 *
3056 * By supplying zeroes for u and v, the topocentric part of the
3057 * model can be nullified, and the function will return the Fairhead
3058 * & Bretagnon result alone.
3059 *
3060 * <li> During the interval 1950-2050, the absolute accuracy is better
3061 * than +/- 3 nanoseconds relative to time ephemerides obtained by
3062 * direct numerical integrations based on the JPL DE405 solar system
3063 * ephemeris.
3064 *
3065 * <li> It must be stressed that the present function is merely a model,
3066 * and that numerical integration of solar-system ephemerides is the
3067 * definitive method for predicting the relationship between TCG and
3068 * TCB and hence between TT and TDB.
3069 *</ol>
3070 *<p>References:
3071 *
3072 * <p>Fairhead, L., & Bretagnon, P., Astron.Astrophys., 229, 240-247
3073 * (1990).
3074 *
3075 * <p>IAU 2006 Resolution 3.
3076 *
3077 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
3078 * IERS Technical Note No. 32, BKG (2004)
3079 *
3080 * <p>Moyer, T.D., Cel.Mech., 23, 33 (1981).
3081 *
3082 * <p>Murray, C.A., Vectorial Astrometry, Adam Hilger (1983).
3083 *
3084 * <p>Seidelmann, P.K. et al., Explanatory Supplement to the
3085 * Astronomical Almanac, Chapter 2, University Science Books (1992).
3086 *
3087 * <p>Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
3088 * Francou, G. & Laskar, J., Astron.Astrophys., 282, 663-683 (1994).
3089 *
3090 *@version 2009 December 17
3091 *
3092 * @since Release 20101201
3093 *
3094 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
3095 */
3096 public static double jauDtdb(double date1, double date2,
3097 double ut, double elong, double u, double v)
3098 {
3099 double t, tsol, w, elsun, emsun, d, elj, els, wt, w0, w1, w2, w3, w4,
3100 wf, wj;
3101 int j;
3102
3103 /*
3104 * =====================
3105 * Fairhead et al. model
3106 * =====================
3107 *
3108 * 787 sets of three coefficients.
3109 *
3110 * Each set is
3111 * amplitude (microseconds)
3112 * frequency (radians per Julian millennium since J2000.0)
3113 * phase (radians)
3114 *
3115 * Sets 1-474 are the T**0 terms
3116 * " 475-679 " " T**1
3117 * " 680-764 " " T**2
3118 * " 765-784 " " T**3
3119 * " 785-787 " " T**4
3120 */
3121
3122 final double fairhd[][] = {
3123 /* 1, 10 */
3124 { 1656.674564e-6, 6283.075849991, 6.240054195 },
3125 { 22.417471e-6, 5753.384884897, 4.296977442 },
3126 { 13.839792e-6, 12566.151699983, 6.196904410 },
3127 { 4.770086e-6, 529.690965095, 0.444401603 },
3128 { 4.676740e-6, 6069.776754553, 4.021195093 },
3129 { 2.256707e-6, 213.299095438, 5.543113262 },
3130 { 1.694205e-6, -3.523118349, 5.025132748 },
3131 { 1.554905e-6, 77713.771467920, 5.198467090 },
3132 { 1.276839e-6, 7860.419392439, 5.988822341 },
3133 { 1.193379e-6, 5223.693919802, 3.649823730 },
3134 /* 11, 20 */
3135 { 1.115322e-6, 3930.209696220, 1.422745069 },
3136 { 0.794185e-6, 11506.769769794, 2.322313077 },
3137 { 0.447061e-6, 26.298319800, 3.615796498 },
3138 { 0.435206e-6, -398.149003408, 4.349338347 },
3139 { 0.600309e-6, 1577.343542448, 2.678271909 },
3140 { 0.496817e-6, 6208.294251424, 5.696701824 },
3141 { 0.486306e-6, 5884.926846583, 0.520007179 },
3142 { 0.432392e-6, 74.781598567, 2.435898309 },
3143 { 0.468597e-6, 6244.942814354, 5.866398759 },
3144 { 0.375510e-6, 5507.553238667, 4.103476804 },
3145 /* 21, 30 */
3146 { 0.243085e-6, -775.522611324, 3.651837925 },
3147 { 0.173435e-6, 18849.227549974, 6.153743485 },
3148 { 0.230685e-6, 5856.477659115, 4.773852582 },
3149 { 0.203747e-6, 12036.460734888, 4.333987818 },
3150 { 0.143935e-6, -796.298006816, 5.957517795 },
3151 { 0.159080e-6, 10977.078804699, 1.890075226 },
3152 { 0.119979e-6, 38.133035638, 4.551585768 },
3153 { 0.118971e-6, 5486.777843175, 1.914547226 },
3154 { 0.116120e-6, 1059.381930189, 0.873504123 },
3155 { 0.137927e-6, 11790.629088659, 1.135934669 },
3156 /* 31, 40 */
3157 { 0.098358e-6, 2544.314419883, 0.092793886 },
3158 { 0.101868e-6, -5573.142801634, 5.984503847 },
3159 { 0.080164e-6, 206.185548437, 2.095377709 },
3160 { 0.079645e-6, 4694.002954708, 2.949233637 },
3161 { 0.062617e-6, 20.775395492, 2.654394814 },
3162 { 0.075019e-6, 2942.463423292, 4.980931759 },
3163 { 0.064397e-6, 5746.271337896, 1.280308748 },
3164 { 0.063814e-6, 5760.498431898, 4.167901731 },
3165 { 0.048042e-6, 2146.165416475, 1.495846011 },
3166 { 0.048373e-6, 155.420399434, 2.251573730 },
3167 /* 41, 50 */
3168 { 0.058844e-6, 426.598190876, 4.839650148 },
3169 { 0.046551e-6, -0.980321068, 0.921573539 },
3170 { 0.054139e-6, 17260.154654690, 3.411091093 },
3171 { 0.042411e-6, 6275.962302991, 2.869567043 },
3172 { 0.040184e-6, -7.113547001, 3.565975565 },
3173 { 0.036564e-6, 5088.628839767, 3.324679049 },
3174 { 0.040759e-6, 12352.852604545, 3.981496998 },
3175 { 0.036507e-6, 801.820931124, 6.248866009 },
3176 { 0.036955e-6, 3154.687084896, 5.071801441 },
3177 { 0.042732e-6, 632.783739313, 5.720622217 },
3178 /* 51, 60 */
3179 { 0.042560e-6, 161000.685737473, 1.270837679 },
3180 { 0.040480e-6, 15720.838784878, 2.546610123 },
3181 { 0.028244e-6, -6286.598968340, 5.069663519 },
3182 { 0.033477e-6, 6062.663207553, 4.144987272 },
3183 { 0.034867e-6, 522.577418094, 5.210064075 },
3184 { 0.032438e-6, 6076.890301554, 0.749317412 },
3185 { 0.030215e-6, 7084.896781115, 3.389610345 },
3186 { 0.029247e-6, -71430.695617928, 4.183178762 },
3187 { 0.033529e-6, 9437.762934887, 2.404714239 },
3188 { 0.032423e-6, 8827.390269875, 5.541473556 },
3189 /* 61, 70 */
3190 { 0.027567e-6, 6279.552731642, 5.040846034 },
3191 { 0.029862e-6, 12139.553509107, 1.770181024 },
3192 { 0.022509e-6, 10447.387839604, 1.460726241 },
3193 { 0.020937e-6, 8429.241266467, 0.652303414 },
3194 { 0.020322e-6, 419.484643875, 3.735430632 },
3195 { 0.024816e-6, -1194.447010225, 1.087136918 },
3196 { 0.025196e-6, 1748.016413067, 2.901883301 },
3197 { 0.021691e-6, 14143.495242431, 5.952658009 },
3198 { 0.017673e-6, 6812.766815086, 3.186129845 },
3199 { 0.022567e-6, 6133.512652857, 3.307984806 },
3200 /* 71, 80 */
3201 { 0.016155e-6, 10213.285546211, 1.331103168 },
3202 { 0.014751e-6, 1349.867409659, 4.308933301 },
3203 { 0.015949e-6, -220.412642439, 4.005298270 },
3204 { 0.015974e-6, -2352.866153772, 6.145309371 },
3205 { 0.014223e-6, 17789.845619785, 2.104551349 },
3206 { 0.017806e-6, 73.297125859, 3.475975097 },
3207 { 0.013671e-6, -536.804512095, 5.971672571 },
3208 { 0.011942e-6, 8031.092263058, 2.053414715 },
3209 { 0.014318e-6, 16730.463689596, 3.016058075 },
3210 { 0.012462e-6, 103.092774219, 1.737438797 },
3211 /* 81, 90 */
3212 { 0.010962e-6, 3.590428652, 2.196567739 },
3213 { 0.015078e-6, 19651.048481098, 3.969480770 },
3214 { 0.010396e-6, 951.718406251, 5.717799605 },
3215 { 0.011707e-6, -4705.732307544, 2.654125618 },
3216 { 0.010453e-6, 5863.591206116, 1.913704550 },
3217 { 0.012420e-6, 4690.479836359, 4.734090399 },
3218 { 0.011847e-6, 5643.178563677, 5.489005403 },
3219 { 0.008610e-6, 3340.612426700, 3.661698944 },
3220 { 0.011622e-6, 5120.601145584, 4.863931876 },
3221 { 0.010825e-6, 553.569402842, 0.842715011 },
3222 /* 91, 100 */
3223 { 0.008666e-6, -135.065080035, 3.293406547 },
3224 { 0.009963e-6, 149.563197135, 4.870690598 },
3225 { 0.009858e-6, 6309.374169791, 1.061816410 },
3226 { 0.007959e-6, 316.391869657, 2.465042647 },
3227 { 0.010099e-6, 283.859318865, 1.942176992 },
3228 { 0.007147e-6, -242.728603974, 3.661486981 },
3229 { 0.007505e-6, 5230.807466803, 4.920937029 },
3230 { 0.008323e-6, 11769.853693166, 1.229392026 },
3231 { 0.007490e-6, -6256.777530192, 3.658444681 },
3232 { 0.009370e-6, 149854.400134205, 0.673880395 },
3233 /* 101, 110 */
3234 { 0.007117e-6, 38.027672636, 5.294249518 },
3235 { 0.007857e-6, 12168.002696575, 0.525733528 },
3236 { 0.007019e-6, 6206.809778716, 0.837688810 },
3237 { 0.006056e-6, 955.599741609, 4.194535082 },
3238 { 0.008107e-6, 13367.972631107, 3.793235253 },
3239 { 0.006731e-6, 5650.292110678, 5.639906583 },
3240 { 0.007332e-6, 36.648562930, 0.114858677 },
3241 { 0.006366e-6, 4164.311989613, 2.262081818 },
3242 { 0.006858e-6, 5216.580372801, 0.642063318 },
3243 { 0.006919e-6, 6681.224853400, 6.018501522 },
3244 /* 111, 120 */
3245 { 0.006826e-6, 7632.943259650, 3.458654112 },
3246 { 0.005308e-6, -1592.596013633, 2.500382359 },
3247 { 0.005096e-6, 11371.704689758, 2.547107806 },
3248 { 0.004841e-6, 5333.900241022, 0.437078094 },
3249 { 0.005582e-6, 5966.683980335, 2.246174308 },
3250 { 0.006304e-6, 11926.254413669, 2.512929171 },
3251 { 0.006603e-6, 23581.258177318, 5.393136889 },
3252 { 0.005123e-6, -1.484472708, 2.999641028 },
3253 { 0.004648e-6, 1589.072895284, 1.275847090 },
3254 { 0.005119e-6, 6438.496249426, 1.486539246 },
3255 /* 121, 130 */
3256 { 0.004521e-6, 4292.330832950, 6.140635794 },
3257 { 0.005680e-6, 23013.539539587, 4.557814849 },
3258 { 0.005488e-6, -3.455808046, 0.090675389 },
3259 { 0.004193e-6, 7234.794256242, 4.869091389 },
3260 { 0.003742e-6, 7238.675591600, 4.691976180 },
3261 { 0.004148e-6, -110.206321219, 3.016173439 },
3262 { 0.004553e-6, 11499.656222793, 5.554998314 },
3263 { 0.004892e-6, 5436.993015240, 1.475415597 },
3264 { 0.004044e-6, 4732.030627343, 1.398784824 },
3265 { 0.004164e-6, 12491.370101415, 5.650931916 },
3266 /* 131, 140 */
3267 { 0.004349e-6, 11513.883316794, 2.181745369 },
3268 { 0.003919e-6, 12528.018664345, 5.823319737 },
3269 { 0.003129e-6, 6836.645252834, 0.003844094 },
3270 { 0.004080e-6, -7058.598461315, 3.690360123 },
3271 { 0.003270e-6, 76.266071276, 1.517189902 },
3272 { 0.002954e-6, 6283.143160294, 4.447203799 },
3273 { 0.002872e-6, 28.449187468, 1.158692983 },
3274 { 0.002881e-6, 735.876513532, 0.349250250 },
3275 { 0.003279e-6, 5849.364112115, 4.893384368 },
3276 { 0.003625e-6, 6209.778724132, 1.473760578 },
3277 /* 141, 150 */
3278 { 0.003074e-6, 949.175608970, 5.185878737 },
3279 { 0.002775e-6, 9917.696874510, 1.030026325 },
3280 { 0.002646e-6, 10973.555686350, 3.918259169 },
3281 { 0.002575e-6, 25132.303399966, 6.109659023 },
3282 { 0.003500e-6, 263.083923373, 1.892100742 },
3283 { 0.002740e-6, 18319.536584880, 4.320519510 },
3284 { 0.002464e-6, 202.253395174, 4.698203059 },
3285 { 0.002409e-6, 2.542797281, 5.325009315 },
3286 { 0.003354e-6, -90955.551694697, 1.942656623 },
3287 { 0.002296e-6, 6496.374945429, 5.061810696 },
3288 /* 151, 160 */
3289 { 0.003002e-6, 6172.869528772, 2.797822767 },
3290 { 0.003202e-6, 27511.467873537, 0.531673101 },
3291 { 0.002954e-6, -6283.008539689, 4.533471191 },
3292 { 0.002353e-6, 639.897286314, 3.734548088 },
3293 { 0.002401e-6, 16200.772724501, 2.605547070 },
3294 { 0.003053e-6, 233141.314403759, 3.029030662 },
3295 { 0.003024e-6, 83286.914269554, 2.355556099 },
3296 { 0.002863e-6, 17298.182327326, 5.240963796 },
3297 { 0.002103e-6, -7079.373856808, 5.756641637 },
3298 { 0.002303e-6, 83996.847317911, 2.013686814 },
3299 /* 161, 170 */
3300 { 0.002303e-6, 18073.704938650, 1.089100410 },
3301 { 0.002381e-6, 63.735898303, 0.759188178 },
3302 { 0.002493e-6, 6386.168624210, 0.645026535 },
3303 { 0.002366e-6, 3.932153263, 6.215885448 },
3304 { 0.002169e-6, 11015.106477335, 4.845297676 },
3305 { 0.002397e-6, 6243.458341645, 3.809290043 },
3306 { 0.002183e-6, 1162.474704408, 6.179611691 },
3307 { 0.002353e-6, 6246.427287062, 4.781719760 },
3308 { 0.002199e-6, -245.831646229, 5.956152284 },
3309 { 0.001729e-6, 3894.181829542, 1.264976635 },
3310 /* 171, 180 */
3311 { 0.001896e-6, -3128.388765096, 4.914231596 },
3312 { 0.002085e-6, 35.164090221, 1.405158503 },
3313 { 0.002024e-6, 14712.317116458, 2.752035928 },
3314 { 0.001737e-6, 6290.189396992, 5.280820144 },
3315 { 0.002229e-6, 491.557929457, 1.571007057 },
3316 { 0.001602e-6, 14314.168113050, 4.203664806 },
3317 { 0.002186e-6, 454.909366527, 1.402101526 },
3318 { 0.001897e-6, 22483.848574493, 4.167932508 },
3319 { 0.001825e-6, -3738.761430108, 0.545828785 },
3320 { 0.001894e-6, 1052.268383188, 5.817167450 },
3321 /* 181, 190 */
3322 { 0.001421e-6, 20.355319399, 2.419886601 },
3323 { 0.001408e-6, 10984.192351700, 2.732084787 },
3324 { 0.001847e-6, 10873.986030480, 2.903477885 },
3325 { 0.001391e-6, -8635.942003763, 0.593891500 },
3326 { 0.001388e-6, -7.046236698, 1.166145902 },
3327 { 0.001810e-6, -88860.057071188, 0.487355242 },
3328 { 0.001288e-6, -1990.745017041, 3.913022880 },
3329 { 0.001297e-6, 23543.230504682, 3.063805171 },
3330 { 0.001335e-6, -266.607041722, 3.995764039 },
3331 { 0.001376e-6, 10969.965257698, 5.152914309 },
3332 /* 191, 200 */
3333 { 0.001745e-6, 244287.600007027, 3.626395673 },
3334 { 0.001649e-6, 31441.677569757, 1.952049260 },
3335 { 0.001416e-6, 9225.539273283, 4.996408389 },
3336 { 0.001238e-6, 4804.209275927, 5.503379738 },
3337 { 0.001472e-6, 4590.910180489, 4.164913291 },
3338 { 0.001169e-6, 6040.347246017, 5.841719038 },
3339 { 0.001039e-6, 5540.085789459, 2.769753519 },
3340 { 0.001004e-6, -170.672870619, 0.755008103 },
3341 { 0.001284e-6, 10575.406682942, 5.306538209 },
3342 { 0.001278e-6, 71.812653151, 4.713486491 },
3343 /* 201, 210 */
3344 { 0.001321e-6, 18209.330263660, 2.624866359 },
3345 { 0.001297e-6, 21228.392023546, 0.382603541 },
3346 { 0.000954e-6, 6282.095528923, 0.882213514 },
3347 { 0.001145e-6, 6058.731054289, 1.169483931 },
3348 { 0.000979e-6, 5547.199336460, 5.448375984 },
3349 { 0.000987e-6, -6262.300454499, 2.656486959 },
3350 { 0.001070e-6, -154717.609887482, 1.827624012 },
3351 { 0.000991e-6, 4701.116501708, 4.387001801 },
3352 { 0.001155e-6, -14.227094002, 3.042700750 },
3353 { 0.001176e-6, 277.034993741, 3.335519004 },
3354 /* 211, 220 */
3355 { 0.000890e-6, 13916.019109642, 5.601498297 },
3356 { 0.000884e-6, -1551.045222648, 1.088831705 },
3357 { 0.000876e-6, 5017.508371365, 3.969902609 },
3358 { 0.000806e-6, 15110.466119866, 5.142876744 },
3359 { 0.000773e-6, -4136.910433516, 0.022067765 },
3360 { 0.001077e-6, 175.166059800, 1.844913056 },
3361 { 0.000954e-6, -6284.056171060, 0.968480906 },
3362 { 0.000737e-6, 5326.786694021, 4.923831588 },
3363 { 0.000845e-6, -433.711737877, 4.749245231 },
3364 { 0.000819e-6, 8662.240323563, 5.991247817 },
3365 /* 221, 230 */
3366 { 0.000852e-6, 199.072001436, 2.189604979 },
3367 { 0.000723e-6, 17256.631536341, 6.068719637 },
3368 { 0.000940e-6, 6037.244203762, 6.197428148 },
3369 { 0.000885e-6, 11712.955318231, 3.280414875 },
3370 { 0.000706e-6, 12559.038152982, 2.824848947 },
3371 { 0.000732e-6, 2379.164473572, 2.501813417 },
3372 { 0.000764e-6, -6127.655450557, 2.236346329 },
3373 { 0.000908e-6, 131.541961686, 2.521257490 },
3374 { 0.000907e-6, 35371.887265976, 3.370195967 },
3375 { 0.000673e-6, 1066.495477190, 3.876512374 },
3376 /* 231, 240 */
3377 { 0.000814e-6, 17654.780539750, 4.627122566 },
3378 { 0.000630e-6, 36.027866677, 0.156368499 },
3379 { 0.000798e-6, 515.463871093, 5.151962502 },
3380 { 0.000798e-6, 148.078724426, 5.909225055 },
3381 { 0.000806e-6, 309.278322656, 6.054064447 },
3382 { 0.000607e-6, -39.617508346, 2.839021623 },
3383 { 0.000601e-6, 412.371096874, 3.984225404 },
3384 { 0.000646e-6, 11403.676995575, 3.852959484 },
3385 { 0.000704e-6, 13521.751441591, 2.300991267 },
3386 { 0.000603e-6, -65147.619767937, 4.140083146 },
3387 /* 241, 250 */
3388 { 0.000609e-6, 10177.257679534, 0.437122327 },
3389 { 0.000631e-6, 5767.611978898, 4.026532329 },
3390 { 0.000576e-6, 11087.285125918, 4.760293101 },
3391 { 0.000674e-6, 14945.316173554, 6.270510511 },
3392 { 0.000726e-6, 5429.879468239, 6.039606892 },
3393 { 0.000710e-6, 28766.924424484, 5.672617711 },
3394 { 0.000647e-6, 11856.218651625, 3.397132627 },
3395 { 0.000678e-6, -5481.254918868, 6.249666675 },
3396 { 0.000618e-6, 22003.914634870, 2.466427018 },
3397 { 0.000738e-6, 6134.997125565, 2.242668890 },
3398 /* 251, 260 */
3399 { 0.000660e-6, 625.670192312, 5.864091907 },
3400 { 0.000694e-6, 3496.032826134, 2.668309141 },
3401 { 0.000531e-6, 6489.261398429, 1.681888780 },
3402 { 0.000611e-6, -143571.324284214, 2.424978312 },
3403 { 0.000575e-6, 12043.574281889, 4.216492400 },
3404 { 0.000553e-6, 12416.588502848, 4.772158039 },
3405 { 0.000689e-6, 4686.889407707, 6.224271088 },
3406 { 0.000495e-6, 7342.457780181, 3.817285811 },
3407 { 0.000567e-6, 3634.621024518, 1.649264690 },
3408 { 0.000515e-6, 18635.928454536, 3.945345892 },
3409 /* 261, 270 */
3410 { 0.000486e-6, -323.505416657, 4.061673868 },
3411 { 0.000662e-6, 25158.601719765, 1.794058369 },
3412 { 0.000509e-6, 846.082834751, 3.053874588 },
3413 { 0.000472e-6, -12569.674818332, 5.112133338 },
3414 { 0.000461e-6, 6179.983075773, 0.513669325 },
3415 { 0.000641e-6, 83467.156352816, 3.210727723 },
3416 { 0.000520e-6, 10344.295065386, 2.445597761 },
3417 { 0.000493e-6, 18422.629359098, 1.676939306 },
3418 { 0.000478e-6, 1265.567478626, 5.487314569 },
3419 { 0.000472e-6, -18.159247265, 1.999707589 },
3420 /* 271, 280 */
3421 { 0.000559e-6, 11190.377900137, 5.783236356 },
3422 { 0.000494e-6, 9623.688276691, 3.022645053 },
3423 { 0.000463e-6, 5739.157790895, 1.411223013 },
3424 { 0.000432e-6, 16858.482532933, 1.179256434 },
3425 { 0.000574e-6, 72140.628666286, 1.758191830 },
3426 { 0.000484e-6, 17267.268201691, 3.290589143 },
3427 { 0.000550e-6, 4907.302050146, 0.864024298 },
3428 { 0.000399e-6, 14.977853527, 2.094441910 },
3429 { 0.000491e-6, 224.344795702, 0.878372791 },
3430 { 0.000432e-6, 20426.571092422, 6.003829241 },
3431 /* 281, 290 */
3432 { 0.000481e-6, 5749.452731634, 4.309591964 },
3433 { 0.000480e-6, 5757.317038160, 1.142348571 },
3434 { 0.000485e-6, 6702.560493867, 0.210580917 },
3435 { 0.000426e-6, 6055.549660552, 4.274476529 },
3436 { 0.000480e-6, 5959.570433334, 5.031351030 },
3437 { 0.000466e-6, 12562.628581634, 4.959581597 },
3438 { 0.000520e-6, 39302.096962196, 4.788002889 },
3439 { 0.000458e-6, 12132.439962106, 1.880103788 },
3440 { 0.000470e-6, 12029.347187887, 1.405611197 },
3441 { 0.000416e-6, -7477.522860216, 1.082356330 },
3442 /* 291, 300 */
3443 { 0.000449e-6, 11609.862544012, 4.179989585 },
3444 { 0.000465e-6, 17253.041107690, 0.353496295 },
3445 { 0.000362e-6, -4535.059436924, 1.583849576 },
3446 { 0.000383e-6, 21954.157609398, 3.747376371 },
3447 { 0.000389e-6, 17.252277143, 1.395753179 },
3448 { 0.000331e-6, 18052.929543158, 0.566790582 },
3449 { 0.000430e-6, 13517.870106233, 0.685827538 },
3450 { 0.000368e-6, -5756.908003246, 0.731374317 },
3451 { 0.000330e-6, 10557.594160824, 3.710043680 },
3452 { 0.000332e-6, 20199.094959633, 1.652901407 },
3453 /* 301, 310 */
3454 { 0.000384e-6, 11933.367960670, 5.827781531 },
3455 { 0.000387e-6, 10454.501386605, 2.541182564 },
3456 { 0.000325e-6, 15671.081759407, 2.178850542 },
3457 { 0.000318e-6, 138.517496871, 2.253253037 },
3458 { 0.000305e-6, 9388.005909415, 0.578340206 },
3459 { 0.000352e-6, 5749.861766548, 3.000297967 },
3460 { 0.000311e-6, 6915.859589305, 1.693574249 },
3461 { 0.000297e-6, 24072.921469776, 1.997249392 },
3462 { 0.000363e-6, -640.877607382, 5.071820966 },
3463 { 0.000323e-6, 12592.450019783, 1.072262823 },
3464 /* 311, 320 */
3465 { 0.000341e-6, 12146.667056108, 4.700657997 },
3466 { 0.000290e-6, 9779.108676125, 1.812320441 },
3467 { 0.000342e-6, 6132.028180148, 4.322238614 },
3468 { 0.000329e-6, 6268.848755990, 3.033827743 },
3469 { 0.000374e-6, 17996.031168222, 3.388716544 },
3470 { 0.000285e-6, -533.214083444, 4.687313233 },
3471 { 0.000338e-6, 6065.844601290, 0.877776108 },
3472 { 0.000276e-6, 24.298513841, 0.770299429 },
3473 { 0.000336e-6, -2388.894020449, 5.353796034 },
3474 { 0.000290e-6, 3097.883822726, 4.075291557 },
3475 /* 321, 330 */
3476 { 0.000318e-6, 709.933048357, 5.941207518 },
3477 { 0.000271e-6, 13095.842665077, 3.208912203 },
3478 { 0.000331e-6, 6073.708907816, 4.007881169 },
3479 { 0.000292e-6, 742.990060533, 2.714333592 },
3480 { 0.000362e-6, 29088.811415985, 3.215977013 },
3481 { 0.000280e-6, 12359.966151546, 0.710872502 },
3482 { 0.000267e-6, 10440.274292604, 4.730108488 },
3483 { 0.000262e-6, 838.969287750, 1.327720272 },
3484 { 0.000250e-6, 16496.361396202, 0.898769761 },
3485 { 0.000325e-6, 20597.243963041, 0.180044365 },
3486 /* 331, 340 */
3487 { 0.000268e-6, 6148.010769956, 5.152666276 },
3488 { 0.000284e-6, 5636.065016677, 5.655385808 },
3489 { 0.000301e-6, 6080.822454817, 2.135396205 },
3490 { 0.000294e-6, -377.373607916, 3.708784168 },
3491 { 0.000236e-6, 2118.763860378, 1.733578756 },
3492 { 0.000234e-6, 5867.523359379, 5.575209112 },
3493 { 0.000268e-6, -226858.238553767, 0.069432392 },
3494 { 0.000265e-6, 167283.761587465, 4.369302826 },
3495 { 0.000280e-6, 28237.233459389, 5.304829118 },
3496 { 0.000292e-6, 12345.739057544, 4.096094132 },
3497 /* 341, 350 */
3498 { 0.000223e-6, 19800.945956225, 3.069327406 },
3499 { 0.000301e-6, 43232.306658416, 6.205311188 },
3500 { 0.000264e-6, 18875.525869774, 1.417263408 },
3501 { 0.000304e-6, -1823.175188677, 3.409035232 },
3502 { 0.000301e-6, 109.945688789, 0.510922054 },
3503 { 0.000260e-6, 813.550283960, 2.389438934 },
3504 { 0.000299e-6, 316428.228673312, 5.384595078 },
3505 { 0.000211e-6, 5756.566278634, 3.789392838 },
3506 { 0.000209e-6, 5750.203491159, 1.661943545 },
3507 { 0.000240e-6, 12489.885628707, 5.684549045 },
3508 /* 351, 360 */
3509 { 0.000216e-6, 6303.851245484, 3.862942261 },
3510 { 0.000203e-6, 1581.959348283, 5.549853589 },
3511 { 0.000200e-6, 5642.198242609, 1.016115785 },
3512 { 0.000197e-6, -70.849445304, 4.690702525 },
3513 { 0.000227e-6, 6287.008003254, 2.911891613 },
3514 { 0.000197e-6, 533.623118358, 1.048982898 },
3515 { 0.000205e-6, -6279.485421340, 1.829362730 },
3516 { 0.000209e-6, -10988.808157535, 2.636140084 },
3517 { 0.000208e-6, -227.526189440, 4.127883842 },
3518 { 0.000191e-6, 415.552490612, 4.401165650 },
3519 /* 361, 370 */
3520 { 0.000190e-6, 29296.615389579, 4.175658539 },
3521 { 0.000264e-6, 66567.485864652, 4.601102551 },
3522 { 0.000256e-6, -3646.350377354, 0.506364778 },
3523 { 0.000188e-6, 13119.721102825, 2.032195842 },
3524 { 0.000185e-6, -209.366942175, 4.694756586 },
3525 { 0.000198e-6, 25934.124331089, 3.832703118 },
3526 { 0.000195e-6, 4061.219215394, 3.308463427 },
3527 { 0.000234e-6, 5113.487598583, 1.716090661 },
3528 { 0.000188e-6, 1478.866574064, 5.686865780 },
3529 { 0.000222e-6, 11823.161639450, 1.942386641 },
3530 /* 371, 380 */
3531 { 0.000181e-6, 10770.893256262, 1.999482059 },
3532 { 0.000171e-6, 6546.159773364, 1.182807992 },
3533 { 0.000206e-6, 70.328180442, 5.934076062 },
3534 { 0.000169e-6, 20995.392966449, 2.169080622 },
3535 { 0.000191e-6, 10660.686935042, 5.405515999 },
3536 { 0.000228e-6, 33019.021112205, 4.656985514 },
3537 { 0.000184e-6, -4933.208440333, 3.327476868 },
3538 { 0.000220e-6, -135.625325010, 1.765430262 },
3539 { 0.000166e-6, 23141.558382925, 3.454132746 },
3540 { 0.000191e-6, 6144.558353121, 5.020393445 },
3541 /* 381, 390 */
3542 { 0.000180e-6, 6084.003848555, 0.602182191 },
3543 { 0.000163e-6, 17782.732072784, 4.960593133 },
3544 { 0.000225e-6, 16460.333529525, 2.596451817 },
3545 { 0.000222e-6, 5905.702242076, 3.731990323 },
3546 { 0.000204e-6, 227.476132789, 5.636192701 },
3547 { 0.000159e-6, 16737.577236597, 3.600691544 },
3548 { 0.000200e-6, 6805.653268085, 0.868220961 },
3549 { 0.000187e-6, 11919.140866668, 2.629456641 },
3550 { 0.000161e-6, 127.471796607, 2.862574720 },
3551 { 0.000205e-6, 6286.666278643, 1.742882331 },
3552 /* 391, 400 */
3553 { 0.000189e-6, 153.778810485, 4.812372643 },
3554 { 0.000168e-6, 16723.350142595, 0.027860588 },
3555 { 0.000149e-6, 11720.068865232, 0.659721876 },
3556 { 0.000189e-6, 5237.921013804, 5.245313000 },
3557 { 0.000143e-6, 6709.674040867, 4.317625647 },
3558 { 0.000146e-6, 4487.817406270, 4.815297007 },
3559 { 0.000144e-6, -664.756045130, 5.381366880 },
3560 { 0.000175e-6, 5127.714692584, 4.728443327 },
3561 { 0.000162e-6, 6254.626662524, 1.435132069 },
3562 { 0.000187e-6, 47162.516354635, 1.354371923 },
3563 /* 401, 410 */
3564 { 0.000146e-6, 11080.171578918, 3.369695406 },
3565 { 0.000180e-6, -348.924420448, 2.490902145 },
3566 { 0.000148e-6, 151.047669843, 3.799109588 },
3567 { 0.000157e-6, 6197.248551160, 1.284375887 },
3568 { 0.000167e-6, 146.594251718, 0.759969109 },
3569 { 0.000133e-6, -5331.357443741, 5.409701889 },
3570 { 0.000154e-6, 95.979227218, 3.366890614 },
3571 { 0.000148e-6, -6418.140930027, 3.384104996 },
3572 { 0.000128e-6, -6525.804453965, 3.803419985 },
3573 { 0.000130e-6, 11293.470674356, 0.939039445 },
3574 /* 411, 420 */
3575 { 0.000152e-6, -5729.506447149, 0.734117523 },
3576 { 0.000138e-6, 210.117701700, 2.564216078 },
3577 { 0.000123e-6, 6066.595360816, 4.517099537 },
3578 { 0.000140e-6, 18451.078546566, 0.642049130 },
3579 { 0.000126e-6, 11300.584221356, 3.485280663 },
3580 { 0.000119e-6, 10027.903195729, 3.217431161 },
3581 { 0.000151e-6, 4274.518310832, 4.404359108 },
3582 { 0.000117e-6, 6072.958148291, 0.366324650 },
3583 { 0.000165e-6, -7668.637425143, 4.298212528 },
3584 { 0.000117e-6, -6245.048177356, 5.379518958 },
3585 /* 421, 430 */
3586 { 0.000130e-6, -5888.449964932, 4.527681115 },
3587 { 0.000121e-6, -543.918059096, 6.109429504 },
3588 { 0.000162e-6, 9683.594581116, 5.720092446 },
3589 { 0.000141e-6, 6219.339951688, 0.679068671 },
3590 { 0.000118e-6, 22743.409379516, 4.881123092 },
3591 { 0.000129e-6, 1692.165669502, 0.351407289 },
3592 { 0.000126e-6, 5657.405657679, 5.146592349 },
3593 { 0.000114e-6, 728.762966531, 0.520791814 },
3594 { 0.000120e-6, 52.596639600, 0.948516300 },
3595 { 0.000115e-6, 65.220371012, 3.504914846 },
3596 /* 431, 440 */
3597 { 0.000126e-6, 5881.403728234, 5.577502482 },
3598 { 0.000158e-6, 163096.180360983, 2.957128968 },
3599 { 0.000134e-6, 12341.806904281, 2.598576764 },
3600 { 0.000151e-6, 16627.370915377, 3.985702050 },
3601 { 0.000109e-6, 1368.660252845, 0.014730471 },
3602 { 0.000131e-6, 6211.263196841, 0.085077024 },
3603 { 0.000146e-6, 5792.741760812, 0.708426604 },
3604 { 0.000146e-6, -77.750543984, 3.121576600 },
3605 { 0.000107e-6, 5341.013788022, 0.288231904 },
3606 { 0.000138e-6, 6281.591377283, 2.797450317 },
3607 /* 441, 450 */
3608 { 0.000113e-6, -6277.552925684, 2.788904128 },
3609 { 0.000115e-6, -525.758811831, 5.895222200 },
3610 { 0.000138e-6, 6016.468808270, 6.096188999 },
3611 { 0.000139e-6, 23539.707386333, 2.028195445 },
3612 { 0.000146e-6, -4176.041342449, 4.660008502 },
3613 { 0.000107e-6, 16062.184526117, 4.066520001 },
3614 { 0.000142e-6, 83783.548222473, 2.936315115 },
3615 { 0.000128e-6, 9380.959672717, 3.223844306 },
3616 { 0.000135e-6, 6205.325306007, 1.638054048 },
3617 { 0.000101e-6, 2699.734819318, 5.481603249 },
3618 /* 451, 460 */
3619 { 0.000104e-6, -568.821874027, 2.205734493 },
3620 { 0.000103e-6, 6321.103522627, 2.440421099 },
3621 { 0.000119e-6, 6321.208885629, 2.547496264 },
3622 { 0.000138e-6, 1975.492545856, 2.314608466 },
3623 { 0.000121e-6, 137.033024162, 4.539108237 },
3624 { 0.000123e-6, 19402.796952817, 4.538074405 },
3625 { 0.000119e-6, 22805.735565994, 2.869040566 },
3626 { 0.000133e-6, 64471.991241142, 6.056405489 },
3627 { 0.000129e-6, -85.827298831, 2.540635083 },
3628 { 0.000131e-6, 13613.804277336, 4.005732868 },
3629 /* 461, 470 */
3630 { 0.000104e-6, 9814.604100291, 1.959967212 },
3631 { 0.000112e-6, 16097.679950283, 3.589026260 },
3632 { 0.000123e-6, 2107.034507542, 1.728627253 },
3633 { 0.000121e-6, 36949.230808424, 6.072332087 },
3634 { 0.000108e-6, -12539.853380183, 3.716133846 },
3635 { 0.000113e-6, -7875.671863624, 2.725771122 },
3636 { 0.000109e-6, 4171.425536614, 4.033338079 },
3637 { 0.000101e-6, 6247.911759770, 3.441347021 },
3638 { 0.000113e-6, 7330.728427345, 0.656372122 },
3639 { 0.000113e-6, 51092.726050855, 2.791483066 },
3640 /* 471, 480 */
3641 { 0.000106e-6, 5621.842923210, 1.815323326 },
3642 { 0.000101e-6, 111.430161497, 5.711033677 },
3643 { 0.000103e-6, 909.818733055, 2.812745443 },
3644 { 0.000101e-6, 1790.642637886, 1.965746028 },
3645
3646 /* T */
3647 { 102.156724e-6, 6283.075849991, 4.249032005 },
3648 { 1.706807e-6, 12566.151699983, 4.205904248 },
3649 { 0.269668e-6, 213.299095438, 3.400290479 },
3650 { 0.265919e-6, 529.690965095, 5.836047367 },
3651 { 0.210568e-6, -3.523118349, 6.262738348 },
3652 { 0.077996e-6, 5223.693919802, 4.670344204 },
3653 /* 481, 490 */
3654 { 0.054764e-6, 1577.343542448, 4.534800170 },
3655 { 0.059146e-6, 26.298319800, 1.083044735 },
3656 { 0.034420e-6, -398.149003408, 5.980077351 },
3657 { 0.032088e-6, 18849.227549974, 4.162913471 },
3658 { 0.033595e-6, 5507.553238667, 5.980162321 },
3659 { 0.029198e-6, 5856.477659115, 0.623811863 },
3660 { 0.027764e-6, 155.420399434, 3.745318113 },
3661 { 0.025190e-6, 5746.271337896, 2.980330535 },
3662 { 0.022997e-6, -796.298006816, 1.174411803 },
3663 { 0.024976e-6, 5760.498431898, 2.467913690 },
3664 /* 491, 500 */
3665 { 0.021774e-6, 206.185548437, 3.854787540 },
3666 { 0.017925e-6, -775.522611324, 1.092065955 },
3667 { 0.013794e-6, 426.598190876, 2.699831988 },
3668 { 0.013276e-6, 6062.663207553, 5.845801920 },
3669 { 0.011774e-6, 12036.460734888, 2.292832062 },
3670 { 0.012869e-6, 6076.890301554, 5.333425680 },
3671 { 0.012152e-6, 1059.381930189, 6.222874454 },
3672 { 0.011081e-6, -7.113547001, 5.154724984 },
3673 { 0.010143e-6, 4694.002954708, 4.044013795 },
3674 { 0.009357e-6, 5486.777843175, 3.416081409 },
3675 /* 501, 510 */
3676 { 0.010084e-6, 522.577418094, 0.749320262 },
3677 { 0.008587e-6, 10977.078804699, 2.777152598 },
3678 { 0.008628e-6, 6275.962302991, 4.562060226 },
3679 { 0.008158e-6, -220.412642439, 5.806891533 },
3680 { 0.007746e-6, 2544.314419883, 1.603197066 },
3681 { 0.007670e-6, 2146.165416475, 3.000200440 },
3682 { 0.007098e-6, 74.781598567, 0.443725817 },
3683 { 0.006180e-6, -536.804512095, 1.302642751 },
3684 { 0.005818e-6, 5088.628839767, 4.827723531 },
3685 { 0.004945e-6, -6286.598968340, 0.268305170 },
3686 /* 511, 520 */
3687 { 0.004774e-6, 1349.867409659, 5.808636673 },
3688 { 0.004687e-6, -242.728603974, 5.154890570 },
3689 { 0.006089e-6, 1748.016413067, 4.403765209 },
3690 { 0.005975e-6, -1194.447010225, 2.583472591 },
3691 { 0.004229e-6, 951.718406251, 0.931172179 },
3692 { 0.005264e-6, 553.569402842, 2.336107252 },
3693 { 0.003049e-6, 5643.178563677, 1.362634430 },
3694 { 0.002974e-6, 6812.766815086, 1.583012668 },
3695 { 0.003403e-6, -2352.866153772, 2.552189886 },
3696 { 0.003030e-6, 419.484643875, 5.286473844 },
3697 /* 521, 530 */
3698 { 0.003210e-6, -7.046236698, 1.863796539 },
3699 { 0.003058e-6, 9437.762934887, 4.226420633 },
3700 { 0.002589e-6, 12352.852604545, 1.991935820 },
3701 { 0.002927e-6, 5216.580372801, 2.319951253 },
3702 { 0.002425e-6, 5230.807466803, 3.084752833 },
3703 { 0.002656e-6, 3154.687084896, 2.487447866 },
3704 { 0.002445e-6, 10447.387839604, 2.347139160 },
3705 { 0.002990e-6, 4690.479836359, 6.235872050 },
3706 { 0.002890e-6, 5863.591206116, 0.095197563 },
3707 { 0.002498e-6, 6438.496249426, 2.994779800 },
3708 /* 531, 540 */
3709 { 0.001889e-6, 8031.092263058, 3.569003717 },
3710 { 0.002567e-6, 801.820931124, 3.425611498 },
3711 { 0.001803e-6, -71430.695617928, 2.192295512 },
3712 { 0.001782e-6, 3.932153263, 5.180433689 },
3713 { 0.001694e-6, -4705.732307544, 4.641779174 },
3714 { 0.001704e-6, -1592.596013633, 3.997097652 },
3715 { 0.001735e-6, 5849.364112115, 0.417558428 },
3716 { 0.001643e-6, 8429.241266467, 2.180619584 },
3717 { 0.001680e-6, 38.133035638, 4.164529426 },
3718 { 0.002045e-6, 7084.896781115, 0.526323854 },
3719 /* 541, 550 */
3720 { 0.001458e-6, 4292.330832950, 1.356098141 },
3721 { 0.001437e-6, 20.355319399, 3.895439360 },
3722 { 0.001738e-6, 6279.552731642, 0.087484036 },
3723 { 0.001367e-6, 14143.495242431, 3.987576591 },
3724 { 0.001344e-6, 7234.794256242, 0.090454338 },
3725 { 0.001438e-6, 11499.656222793, 0.974387904 },
3726 { 0.001257e-6, 6836.645252834, 1.509069366 },
3727 { 0.001358e-6, 11513.883316794, 0.495572260 },
3728 { 0.001628e-6, 7632.943259650, 4.968445721 },
3729 { 0.001169e-6, 103.092774219, 2.838496795 },
3730 /* 551, 560 */
3731 { 0.001162e-6, 4164.311989613, 3.408387778 },
3732 { 0.001092e-6, 6069.776754553, 3.617942651 },
3733 { 0.001008e-6, 17789.845619785, 0.286350174 },
3734 { 0.001008e-6, 639.897286314, 1.610762073 },
3735 { 0.000918e-6, 10213.285546211, 5.532798067 },
3736 { 0.001011e-6, -6256.777530192, 0.661826484 },
3737 { 0.000753e-6, 16730.463689596, 3.905030235 },
3738 { 0.000737e-6, 11926.254413669, 4.641956361 },
3739 { 0.000694e-6, 3340.612426700, 2.111120332 },
3740 { 0.000701e-6, 3894.181829542, 2.760823491 },
3741 /* 561, 570 */
3742 { 0.000689e-6, -135.065080035, 4.768800780 },
3743 { 0.000700e-6, 13367.972631107, 5.760439898 },
3744 { 0.000664e-6, 6040.347246017, 1.051215840 },
3745 { 0.000654e-6, 5650.292110678, 4.911332503 },
3746 { 0.000788e-6, 6681.224853400, 4.699648011 },
3747 { 0.000628e-6, 5333.900241022, 5.024608847 },
3748 { 0.000755e-6, -110.206321219, 4.370971253 },
3749 { 0.000628e-6, 6290.189396992, 3.660478857 },
3750 { 0.000635e-6, 25132.303399966, 4.121051532 },
3751 { 0.000534e-6, 5966.683980335, 1.173284524 },
3752 /* 571, 580 */
3753 { 0.000543e-6, -433.711737877, 0.345585464 },
3754 { 0.000517e-6, -1990.745017041, 5.414571768 },
3755 { 0.000504e-6, 5767.611978898, 2.328281115 },
3756 { 0.000485e-6, 5753.384884897, 1.685874771 },
3757 { 0.000463e-6, 7860.419392439, 5.297703006 },
3758 { 0.000604e-6, 515.463871093, 0.591998446 },
3759 { 0.000443e-6, 12168.002696575, 4.830881244 },
3760 { 0.000570e-6, 199.072001436, 3.899190272 },
3761 { 0.000465e-6, 10969.965257698, 0.476681802 },
3762 { 0.000424e-6, -7079.373856808, 1.112242763 },
3763 /* 581, 590 */
3764 { 0.000427e-6, 735.876513532, 1.994214480 },
3765 { 0.000478e-6, -6127.655450557, 3.778025483 },
3766 { 0.000414e-6, 10973.555686350, 5.441088327 },
3767 { 0.000512e-6, 1589.072895284, 0.107123853 },
3768 { 0.000378e-6, 10984.192351700, 0.915087231 },
3769 { 0.000402e-6, 11371.704689758, 4.107281715 },
3770 { 0.000453e-6, 9917.696874510, 1.917490952 },
3771 { 0.000395e-6, 149.563197135, 2.763124165 },
3772 { 0.000371e-6, 5739.157790895, 3.112111866 },
3773 { 0.000350e-6, 11790.629088659, 0.440639857 },
3774 /* 591, 600 */
3775 { 0.000356e-6, 6133.512652857, 5.444568842 },
3776 { 0.000344e-6, 412.371096874, 5.676832684 },
3777 { 0.000383e-6, 955.599741609, 5.559734846 },
3778 { 0.000333e-6, 6496.374945429, 0.261537984 },
3779 { 0.000340e-6, 6055.549660552, 5.975534987 },
3780 { 0.000334e-6, 1066.495477190, 2.335063907 },
3781 { 0.000399e-6, 11506.769769794, 5.321230910 },
3782 { 0.000314e-6, 18319.536584880, 2.313312404 },
3783 { 0.000424e-6, 1052.268383188, 1.211961766 },
3784 { 0.000307e-6, 63.735898303, 3.169551388 },
3785 /* 601, 610 */
3786 { 0.000329e-6, 29.821438149, 6.106912080 },
3787 { 0.000357e-6, 6309.374169791, 4.223760346 },
3788 { 0.000312e-6, -3738.761430108, 2.180556645 },
3789 { 0.000301e-6, 309.278322656, 1.499984572 },
3790 { 0.000268e-6, 12043.574281889, 2.447520648 },
3791 { 0.000257e-6, 12491.370101415, 3.662331761 },
3792 { 0.000290e-6, 625.670192312, 1.272834584 },
3793 { 0.000256e-6, 5429.879468239, 1.913426912 },
3794 { 0.000339e-6, 3496.032826134, 4.165930011 },
3795 { 0.000283e-6, 3930.209696220, 4.325565754 },
3796 /* 611, 620 */
3797 { 0.000241e-6, 12528.018664345, 3.832324536 },
3798 { 0.000304e-6, 4686.889407707, 1.612348468 },
3799 { 0.000259e-6, 16200.772724501, 3.470173146 },
3800 { 0.000238e-6, 12139.553509107, 1.147977842 },
3801 { 0.000236e-6, 6172.869528772, 3.776271728 },
3802 { 0.000296e-6, -7058.598461315, 0.460368852 },
3803 { 0.000306e-6, 10575.406682942, 0.554749016 },
3804 { 0.000251e-6, 17298.182327326, 0.834332510 },
3805 { 0.000290e-6, 4732.030627343, 4.759564091 },
3806 { 0.000261e-6, 5884.926846583, 0.298259862 },
3807 /* 621, 630 */
3808 { 0.000249e-6, 5547.199336460, 3.749366406 },
3809 { 0.000213e-6, 11712.955318231, 5.415666119 },
3810 { 0.000223e-6, 4701.116501708, 2.703203558 },
3811 { 0.000268e-6, -640.877607382, 0.283670793 },
3812 { 0.000209e-6, 5636.065016677, 1.238477199 },
3813 { 0.000193e-6, 10177.257679534, 1.943251340 },
3814 { 0.000182e-6, 6283.143160294, 2.456157599 },
3815 { 0.000184e-6, -227.526189440, 5.888038582 },
3816 { 0.000182e-6, -6283.008539689, 0.241332086 },
3817 { 0.000228e-6, -6284.056171060, 2.657323816 },
3818 /* 631, 640 */
3819 { 0.000166e-6, 7238.675591600, 5.930629110 },
3820 { 0.000167e-6, 3097.883822726, 5.570955333 },
3821 { 0.000159e-6, -323.505416657, 5.786670700 },
3822 { 0.000154e-6, -4136.910433516, 1.517805532 },
3823 { 0.000176e-6, 12029.347187887, 3.139266834 },
3824 { 0.000167e-6, 12132.439962106, 3.556352289 },
3825 { 0.000153e-6, 202.253395174, 1.463313961 },
3826 { 0.000157e-6, 17267.268201691, 1.586837396 },
3827 { 0.000142e-6, 83996.847317911, 0.022670115 },
3828 { 0.000152e-6, 17260.154654690, 0.708528947 },
3829 /* 641, 650 */
3830 { 0.000144e-6, 6084.003848555, 5.187075177 },
3831 { 0.000135e-6, 5756.566278634, 1.993229262 },
3832 { 0.000134e-6, 5750.203491159, 3.457197134 },
3833 { 0.000144e-6, 5326.786694021, 6.066193291 },
3834 { 0.000160e-6, 11015.106477335, 1.710431974 },
3835 { 0.000133e-6, 3634.621024518, 2.836451652 },
3836 { 0.000134e-6, 18073.704938650, 5.453106665 },
3837 { 0.000134e-6, 1162.474704408, 5.326898811 },
3838 { 0.000128e-6, 5642.198242609, 2.511652591 },
3839 { 0.000160e-6, 632.783739313, 5.628785365 },
3840 /* 651, 660 */
3841 { 0.000132e-6, 13916.019109642, 0.819294053 },
3842 { 0.000122e-6, 14314.168113050, 5.677408071 },
3843 { 0.000125e-6, 12359.966151546, 5.251984735 },
3844 { 0.000121e-6, 5749.452731634, 2.210924603 },
3845 { 0.000136e-6, -245.831646229, 1.646502367 },
3846 { 0.000120e-6, 5757.317038160, 3.240883049 },
3847 { 0.000134e-6, 12146.667056108, 3.059480037 },
3848 { 0.000137e-6, 6206.809778716, 1.867105418 },
3849 { 0.000141e-6, 17253.041107690, 2.069217456 },
3850 { 0.000129e-6, -7477.522860216, 2.781469314 },
3851 /* 661, 670 */
3852 { 0.000116e-6, 5540.085789459, 4.281176991 },
3853 { 0.000116e-6, 9779.108676125, 3.320925381 },
3854 { 0.000129e-6, 5237.921013804, 3.497704076 },
3855 { 0.000113e-6, 5959.570433334, 0.983210840 },
3856 { 0.000122e-6, 6282.095528923, 2.674938860 },
3857 { 0.000140e-6, -11.045700264, 4.957936982 },
3858 { 0.000108e-6, 23543.230504682, 1.390113589 },
3859 { 0.000106e-6, -12569.674818332, 0.429631317 },
3860 { 0.000110e-6, -266.607041722, 5.501340197 },
3861 { 0.000115e-6, 12559.038152982, 4.691456618 },
3862 /* 671, 680 */
3863 { 0.000134e-6, -2388.894020449, 0.577313584 },
3864 { 0.000109e-6, 10440.274292604, 6.218148717 },
3865 { 0.000102e-6, -543.918059096, 1.477842615 },
3866 { 0.000108e-6, 21228.392023546, 2.237753948 },
3867 { 0.000101e-6, -4535.059436924, 3.100492232 },
3868 { 0.000103e-6, 76.266071276, 5.594294322 },
3869 { 0.000104e-6, 949.175608970, 5.674287810 },
3870 { 0.000101e-6, 13517.870106233, 2.196632348 },
3871 { 0.000100e-6, 11933.367960670, 4.056084160 },
3872
3873 /* T^2 */
3874 { 4.322990e-6, 6283.075849991, 2.642893748 },
3875 /* 681, 690 */
3876 { 0.406495e-6, 0.000000000, 4.712388980 },
3877 { 0.122605e-6, 12566.151699983, 2.438140634 },
3878 { 0.019476e-6, 213.299095438, 1.642186981 },
3879 { 0.016916e-6, 529.690965095, 4.510959344 },
3880 { 0.013374e-6, -3.523118349, 1.502210314 },
3881 { 0.008042e-6, 26.298319800, 0.478549024 },
3882 { 0.007824e-6, 155.420399434, 5.254710405 },
3883 { 0.004894e-6, 5746.271337896, 4.683210850 },
3884 { 0.004875e-6, 5760.498431898, 0.759507698 },
3885 { 0.004416e-6, 5223.693919802, 6.028853166 },
3886 /* 691, 700 */
3887 { 0.004088e-6, -7.113547001, 0.060926389 },
3888 { 0.004433e-6, 77713.771467920, 3.627734103 },
3889 { 0.003277e-6, 18849.227549974, 2.327912542 },
3890 { 0.002703e-6, 6062.663207553, 1.271941729 },
3891 { 0.003435e-6, -775.522611324, 0.747446224 },
3892 { 0.002618e-6, 6076.890301554, 3.633715689 },
3893 { 0.003146e-6, 206.185548437, 5.647874613 },
3894 { 0.002544e-6, 1577.343542448, 6.232904270 },
3895 { 0.002218e-6, -220.412642439, 1.309509946 },
3896 { 0.002197e-6, 5856.477659115, 2.407212349 },
3897 /* 701, 710 */
3898 { 0.002897e-6, 5753.384884897, 5.863842246 },
3899 { 0.001766e-6, 426.598190876, 0.754113147 },
3900 { 0.001738e-6, -796.298006816, 2.714942671 },
3901 { 0.001695e-6, 522.577418094, 2.629369842 },
3902 { 0.001584e-6, 5507.553238667, 1.341138229 },
3903 { 0.001503e-6, -242.728603974, 0.377699736 },
3904 { 0.001552e-6, -536.804512095, 2.904684667 },
3905 { 0.001370e-6, -398.149003408, 1.265599125 },
3906 { 0.001889e-6, -5573.142801634, 4.413514859 },
3907 { 0.001722e-6, 6069.776754553, 2.445966339 },
3908 /* 711, 720 */
3909 { 0.001124e-6, 1059.381930189, 5.041799657 },
3910 { 0.001258e-6, 553.569402842, 3.849557278 },
3911 { 0.000831e-6, 951.718406251, 2.471094709 },
3912 { 0.000767e-6, 4694.002954708, 5.363125422 },
3913 { 0.000756e-6, 1349.867409659, 1.046195744 },
3914 { 0.000775e-6, -11.045700264, 0.245548001 },
3915 { 0.000597e-6, 2146.165416475, 4.543268798 },
3916 { 0.000568e-6, 5216.580372801, 4.178853144 },
3917 { 0.000711e-6, 1748.016413067, 5.934271972 },
3918 { 0.000499e-6, 12036.460734888, 0.624434410 },
3919 /* 721, 730 */
3920 { 0.000671e-6, -1194.447010225, 4.136047594 },
3921 { 0.000488e-6, 5849.364112115, 2.209679987 },
3922 { 0.000621e-6, 6438.496249426, 4.518860804 },
3923 { 0.000495e-6, -6286.598968340, 1.868201275 },
3924 { 0.000456e-6, 5230.807466803, 1.271231591 },
3925 { 0.000451e-6, 5088.628839767, 0.084060889 },
3926 { 0.000435e-6, 5643.178563677, 3.324456609 },
3927 { 0.000387e-6, 10977.078804699, 4.052488477 },
3928 { 0.000547e-6, 161000.685737473, 2.841633844 },
3929 { 0.000522e-6, 3154.687084896, 2.171979966 },
3930 /* 731, 740 */
3931 { 0.000375e-6, 5486.777843175, 4.983027306 },
3932 { 0.000421e-6, 5863.591206116, 4.546432249 },
3933 { 0.000439e-6, 7084.896781115, 0.522967921 },
3934 { 0.000309e-6, 2544.314419883, 3.172606705 },
3935 { 0.000347e-6, 4690.479836359, 1.479586566 },
3936 { 0.000317e-6, 801.820931124, 3.553088096 },
3937 { 0.000262e-6, 419.484643875, 0.606635550 },
3938 { 0.000248e-6, 6836.645252834, 3.014082064 },
3939 { 0.000245e-6, -1592.596013633, 5.519526220 },
3940 { 0.000225e-6, 4292.330832950, 2.877956536 },
3941 /* 741, 750 */
3942 { 0.000214e-6, 7234.794256242, 1.605227587 },
3943 { 0.000205e-6, 5767.611978898, 0.625804796 },
3944 { 0.000180e-6, 10447.387839604, 3.499954526 },
3945 { 0.000229e-6, 199.072001436, 5.632304604 },
3946 { 0.000214e-6, 639.897286314, 5.960227667 },
3947 { 0.000175e-6, -433.711737877, 2.162417992 },
3948 { 0.000209e-6, 515.463871093, 2.322150893 },
3949 { 0.000173e-6, 6040.347246017, 2.556183691 },
3950 { 0.000184e-6, 6309.374169791, 4.732296790 },
3951 { 0.000227e-6, 149854.400134205, 5.385812217 },
3952 /* 751, 760 */
3953 { 0.000154e-6, 8031.092263058, 5.120720920 },
3954 { 0.000151e-6, 5739.157790895, 4.815000443 },
3955 { 0.000197e-6, 7632.943259650, 0.222827271 },
3956 { 0.000197e-6, 74.781598567, 3.910456770 },
3957 { 0.000138e-6, 6055.549660552, 1.397484253 },
3958 { 0.000149e-6, -6127.655450557, 5.333727496 },
3959 { 0.000137e-6, 3894.181829542, 4.281749907 },
3960 { 0.000135e-6, 9437.762934887, 5.979971885 },
3961 { 0.000139e-6, -2352.866153772, 4.715630782 },
3962 { 0.000142e-6, 6812.766815086, 0.513330157 },
3963 /* 761, 770 */
3964 { 0.000120e-6, -4705.732307544, 0.194160689 },
3965 { 0.000131e-6, -71430.695617928, 0.000379226 },
3966 { 0.000124e-6, 6279.552731642, 2.122264908 },
3967 { 0.000108e-6, -6256.777530192, 0.883445696 },
3968
3969 /* T^3 */
3970 { 0.143388e-6, 6283.075849991, 1.131453581 },
3971 { 0.006671e-6, 12566.151699983, 0.775148887 },
3972 { 0.001480e-6, 155.420399434, 0.480016880 },
3973 { 0.000934e-6, 213.299095438, 6.144453084 },
3974 { 0.000795e-6, 529.690965095, 2.941595619 },
3975 { 0.000673e-6, 5746.271337896, 0.120415406 },
3976 /* 771, 780 */
3977 { 0.000672e-6, 5760.498431898, 5.317009738 },
3978 { 0.000389e-6, -220.412642439, 3.090323467 },
3979 { 0.000373e-6, 6062.663207553, 3.003551964 },
3980 { 0.000360e-6, 6076.890301554, 1.918913041 },
3981 { 0.000316e-6, -21.340641002, 5.545798121 },
3982 { 0.000315e-6, -242.728603974, 1.884932563 },
3983 { 0.000278e-6, 206.185548437, 1.266254859 },
3984 { 0.000238e-6, -536.804512095, 4.532664830 },
3985 { 0.000185e-6, 522.577418094, 4.578313856 },
3986 { 0.000245e-6, 18849.227549974, 0.587467082 },
3987 /* 781, 787 */
3988 { 0.000180e-6, 426.598190876, 5.151178553 },
3989 { 0.000200e-6, 553.569402842, 5.355983739 },
3990 { 0.000141e-6, 5223.693919802, 1.336556009 },
3991 { 0.000104e-6, 5856.477659115, 4.239842759 },
3992
3993 /* T^4 */
3994 { 0.003826e-6, 6283.075849991, 5.705257275 },
3995 { 0.000303e-6, 12566.151699983, 5.407132842 },
3996 { 0.000209e-6, 155.420399434, 1.989815753 }
3997 };
3998
3999
4000 /* Time since J2000.0 in Julian millennia. */
4001 t = ((date1 - DJ00) + date2) / DJM;
4002
4003 /* ================= */
4004 /* Topocentric terms */
4005 /* ================= */
4006
4007 /* Convert UT to local solar time in radians. */
4008 tsol = fmod(ut, 1.0) * D2PI + elong;
4009
4010 /* FUNDAMENTAL ARGUMENTS: Simon et al. 1994. */
4011
4012 /* Combine time argument (millennia) with deg/arcsec factor. */
4013 w = t / 3600.0;
4014
4015 /* Sun Mean Longitude. */
4016 elsun = fmod(280.46645683 + 1296027711.03429 * w, 360.0) * DD2R;
4017
4018 /* Sun Mean Anomaly. */
4019 emsun = fmod(357.52910918 + 1295965810.481 * w, 360.0) * DD2R;
4020
4021 /* Mean Elongation of Moon from Sun. */
4022 d = fmod(297.85019547 + 16029616012.090 * w, 360.0) * DD2R;
4023
4024 /* Mean Longitude of Jupiter. */
4025 elj = fmod(34.35151874 + 109306899.89453 * w, 360.0) * DD2R;
4026
4027 /* Mean Longitude of Saturn. */
4028 els = fmod(50.07744430 + 44046398.47038 * w, 360.0) * DD2R;
4029
4030 /* TOPOCENTRIC TERMS: Moyer 1981 and Murray 1983. */
4031 wt = + 0.00029e-10 * u * sin(tsol + elsun - els)
4032 + 0.00100e-10 * u * sin(tsol - 2.0 * emsun)
4033 + 0.00133e-10 * u * sin(tsol - d)
4034 + 0.00133e-10 * u * sin(tsol + elsun - elj)
4035 - 0.00229e-10 * u * sin(tsol + 2.0 * elsun + emsun)
4036 - 0.02200e-10 * v * cos(elsun + emsun)
4037 + 0.05312e-10 * u * sin(tsol - emsun)
4038 - 0.13677e-10 * u * sin(tsol + 2.0 * elsun)
4039 - 1.31840e-10 * v * cos(elsun)
4040 + 3.17679e-10 * u * sin(tsol);
4041
4042 /* ===================== */
4043 /* Fairhead et al. model */
4044 /* ===================== */
4045
4046 /* T**0 */
4047 w0 = 0;
4048 for (j = 473; j >= 0; j--) {
4049 w0 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]);
4050 }
4051
4052 /* T**1 */
4053 w1 = 0;
4054 for (j = 678; j >= 474; j--) {
4055 w1 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]);
4056 }
4057
4058 /* T**2 */
4059 w2 = 0;
4060 for (j = 763; j >= 679; j--) {
4061 w2 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]);
4062 }
4063
4064 /* T**3 */
4065 w3 = 0;
4066 for (j = 783; j >= 764; j--) {
4067 w3 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]);
4068 }
4069
4070 /* T**4 */
4071 w4 = 0;
4072 for (j = 786; j >= 784; j--) {
4073 w4 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]);
4074 }
4075
4076 /* Multiply by powers of T and combine. */
4077 wf = t * (t * (t * (t * w4 + w3) + w2) + w1) + w0;
4078
4079 /* Adjustments to use JPL planetary masses instead of IAU. */
4080 wj = 0.00065e-6 * sin(6069.776754 * t + 4.021194) +
4081 0.00033e-6 * sin( 213.299095 * t + 5.543132) +
4082 (-0.00196e-6 * sin(6208.294251 * t + 5.696701)) +
4083 (-0.00173e-6 * sin( 74.781599 * t + 2.435900)) +
4084 0.03638e-6 * t * t;
4085
4086 /* ============ */
4087 /* Final result */
4088 /* ============ */
4089
4090 /* TDB-TT in seconds. */
4091 w = wt + wf + wj;
4092
4093 return w;
4094
4095 }
4096
4097
4098 /**
4099 * The equation of the equinoxes, compatible with IAU 2000 resolutions,
4100 * given the nutation in longitude and the mean obliquity.
4101 *
4102 *<p>This function is derived from the International Astronomical Union's
4103 * SOFA (Standards Of Fundamental Astronomy) software collection.
4104 *
4105 *<p>Status: canonical model.
4106 *
4107 *<!-- Given: -->
4108 * @param date1 double TT as a 2-part Julian Date (Note 1)
4109 * @param date2 double TT as a 2-part Julian Date (Note 1)
4110 * @param epsa double mean obliquity (Note 2)
4111 * @param dpsi double nutation in longitude (Note 3)
4112 *
4113 * <!-- Returned (function value): -->
4114 * @return double equation of the equinoxes (Note 4)
4115 *
4116 * <p>Notes:
4117 * <ol>
4118 *
4119 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
4120 * convenient way between the two arguments. For example,
4121 * JD(TT)=2450123.7 could be expressed in any of these ways,
4122 * among others:
4123 *<pre>
4124 * date1 date2
4125 *
4126 * 2450123.7 0.0 (JD method)
4127 * 2451545.0 -1421.3 (J2000 method)
4128 * 2400000.5 50123.2 (MJD method)
4129 * 2450123.5 0.2 (date & time method)
4130 *</pre>
4131 * The JD method is the most natural and convenient to use in
4132 * cases where the loss of several decimal digits of resolution
4133 * is acceptable. The J2000 method is best matched to the way
4134 * the argument is handled internally and will deliver the
4135 * optimum resolution. The MJD method and the date & time methods
4136 * are both good compromises between resolution and convenience.
4137 *
4138 * <li> The obliquity, in radians, is mean of date.
4139 *
4140 * <li> The result, which is in radians, operates in the following sense:
4141 *
4142 * Greenwich apparent ST = GMST + equation of the equinoxes
4143 *
4144 * <li> The result is compatible with the IAU 2000 resolutions. For
4145 * further details, see IERS Conventions 2003 and Capitaine et al.
4146 * (2002).
4147 *</ol>
4148 *<p>Called:<ul>
4149 * <li>{@link #jauEect00} equation of the equinoxes complementary terms
4150 * </ul>
4151 *<p>
4152 *
4153 * <p>Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
4154 * implement the IAU 2000 definition of UT1", Astronomy &
4155 * Astrophysics, 406, 1135-1149 (2003)
4156 *
4157 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
4158 * IERS Technical Note No. 32, BKG (2004)
4159 *
4160 *@version 2008 May 16
4161 *
4162 * @since Release 20101201
4163 *
4164 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
4165 */
4166 public static double jauEe00(double date1, double date2, double epsa, double dpsi)
4167 {
4168 double ee;
4169
4170
4171 /* Equation of the equinoxes. */
4172 ee = dpsi * cos(epsa) + jauEect00(date1, date2);
4173
4174 return ee;
4175
4176 }
4177
4178
4179 /**
4180 * Equation of the equinoxes, compatible with IAU 2000 resolutions.
4181 *
4182 *<p>This function is derived from the International Astronomical Union's
4183 * SOFA (Standards Of Fundamental Astronomy) software collection.
4184 *
4185 *<p>Status: support function.
4186 *
4187 *<!-- Given: -->
4188 * @param date1 double TT as a 2-part Julian Date (Note 1)
4189 * @param date2 double TT as a 2-part Julian Date (Note 1)
4190 *
4191 * <!-- Returned (function value): -->
4192 * @return double equation of the equinoxes (Note 2)
4193 *
4194 * <p>Notes:
4195 * <ol>
4196 *
4197 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
4198 * convenient way between the two arguments. For example,
4199 * JD(TT)=2450123.7 could be expressed in any of these ways,
4200 * among others:
4201 *<pre>
4202 * date1 date2
4203 *
4204 * 2450123.7 0.0 (JD method)
4205 * 2451545.0 -1421.3 (J2000 method)
4206 * 2400000.5 50123.2 (MJD method)
4207 * 2450123.5 0.2 (date & time method)
4208 *</pre>
4209 * The JD method is the most natural and convenient to use in
4210 * cases where the loss of several decimal digits of resolution
4211 * is acceptable. The J2000 method is best matched to the way
4212 * the argument is handled internally and will deliver the
4213 * optimum resolution. The MJD method and the date & time methods
4214 * are both good compromises between resolution and convenience.
4215 *
4216 * <li> The result, which is in radians, operates in the following sense:
4217 *
4218 * Greenwich apparent ST = GMST + equation of the equinoxes
4219 *
4220 * <li> The result is compatible with the IAU 2000 resolutions. For
4221 * further details, see IERS Conventions 2003 and Capitaine et al.
4222 * (2002).
4223 *</ol>
4224 *<p>Called:<ul>
4225 * <li>{@link #jauPr00} IAU 2000 precession adjustments
4226 * <li>{@link #jauObl80} mean obliquity, IAU 1980
4227 * <li>{@link #jauNut00a} nutation, IAU 2000A
4228 * <li>{@link #jauEe00} equation of the equinoxes, IAU 2000
4229 * </ul>
4230 *<p>References:
4231 *
4232 * <p>Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
4233 * implement the IAU 2000 definition of UT1", Astronomy &
4234 * Astrophysics, 406, 1135-1149 (2003).
4235 *
4236 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
4237 * IERS Technical Note No. 32, BKG (2004).
4238 *
4239 *@version 2008 May 16
4240 *
4241 * @since Release 20101201
4242 *
4243 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
4244 */
4245 public static double jauEe00a(double date1, double date2)
4246 {
4247 double epsa, ee;
4248
4249
4250 /* IAU 2000 precession-rate adjustments. */
4251 PrecessionDeltaTerms nutd = jauPr00(date1, date2);
4252
4253 /* Mean obliquity, consistent with IAU 2000 precession-nutation. */
4254 epsa = jauObl80(date1, date2) + nutd.depspr;
4255
4256 /* Nutation in longitude. */
4257 NutationTerms nut = jauNut00a(date1, date2);
4258
4259 /* Equation of the equinoxes. */
4260 ee = jauEe00(date1, date2, epsa, nut.dpsi);
4261
4262 return ee;
4263
4264 }
4265
4266
4267 /**
4268 * Equation of the equinoxes, compatible with IAU 2000 resolutions but
4269 * using the truncated nutation model IAU 2000B.
4270 *
4271 *<p>This function is derived from the International Astronomical Union's
4272 * SOFA (Standards Of Fundamental Astronomy) software collection.
4273 *
4274 *<p>Status: support function.
4275 *
4276 *<!-- Given: -->
4277 * @param date1 double TT as a 2-part Julian Date (Note 1)
4278 * @param date2 double TT as a 2-part Julian Date (Note 1)
4279 *
4280 * <!-- Returned (function value): -->
4281 * @return double equation of the equinoxes (Note 2)
4282 *
4283 * <p>Notes:
4284 * <ol>
4285 *
4286 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
4287 * convenient way between the two arguments. For example,
4288 * JD(TT)=2450123.7 could be expressed in any of these ways,
4289 * among others:
4290 *<pre>
4291 * date1 date2
4292 *
4293 * 2450123.7 0.0 (JD method)
4294 * 2451545.0 -1421.3 (J2000 method)
4295 * 2400000.5 50123.2 (MJD method)
4296 * 2450123.5 0.2 (date & time method)
4297 *</pre>
4298 * The JD method is the most natural and convenient to use in
4299 * cases where the loss of several decimal digits of resolution
4300 * is acceptable. The J2000 method is best matched to the way
4301 * the argument is handled internally and will deliver the
4302 * optimum resolution. The MJD method and the date & time methods
4303 * are both good compromises between resolution and convenience.
4304 *
4305 * <li> The result, which is in radians, operates in the following sense:
4306 *
4307 * Greenwich apparent ST = GMST + equation of the equinoxes
4308 *
4309 * <li> The result is compatible with the IAU 2000 resolutions except
4310 * that accuracy has been compromised for the sake of speed. For
4311 * further details, see McCarthy & Luzum (2001), IERS Conventions
4312 * 2003 and Capitaine et al. (2003).
4313 *</ol>
4314 *<p>Called:<ul>
4315 * <li>{@link #jauPr00} IAU 2000 precession adjustments
4316 * <li>{@link #jauObl80} mean obliquity, IAU 1980
4317 * <li>{@link #jauNut00b} nutation, IAU 2000B
4318 * <li>{@link #jauEe00} equation of the equinoxes, IAU 2000
4319 * </ul>
4320 *<p>
4321 *
4322 * <p>Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
4323 * implement the IAU 2000 definition of UT1", Astronomy &
4324 * Astrophysics, 406, 1135-1149 (2003)
4325 *
4326 * <p>McCarthy, D.D. & Luzum, B.J., "An abridged model of the
4327 * precession-nutation of the celestial pole", Celestial Mechanics &
4328 * Dynamical Astronomy, 85, 37-49 (2003)
4329 *
4330 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
4331 * IERS Technical Note No. 32, BKG (2004)
4332 *
4333 *@version 2008 May 18
4334 *
4335 * @since Release 20101201
4336 *
4337 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
4338 */
4339 public static double jauEe00b(double date1, double date2)
4340 {
4341 double ee;
4342
4343
4344 /* IAU 2000 precession-rate adjustments. */
4345 PrecessionDeltaTerms nutd = jauPr00(date1, date2);
4346
4347 /* Mean obliquity, consistent with IAU 2000 precession-nutation. */
4348 double epsa = jauObl80(date1, date2) + nutd.depspr;
4349
4350 /* Nutation in longitude. dpsi, deps*/
4351 NutationTerms nut = jauNut00b(date1, date2 );
4352
4353 /* Equation of the equinoxes. */
4354 ee = jauEe00(date1, date2, epsa, nut.dpsi);
4355
4356 return ee;
4357
4358 }
4359
4360 /**
4361 * Equation of the equinoxes, compatible with IAU 2000 resolutions and
4362 * IAU 2006/2000A precession-nutation.
4363 *
4364 *<p>This function is derived from the International Astronomical Union's
4365 * SOFA (Standards Of Fundamental Astronomy) software collection.
4366 *
4367 *<p>Status: support function.
4368 *
4369 *<!-- Given: -->
4370 * @param date1 double TT as a 2-part Julian Date (Note 1)
4371 * @param date2 double TT as a 2-part Julian Date (Note 1)
4372 *
4373 * <!-- Returned (function value): -->
4374 * @return double equation of the equinoxes (Note 2)
4375 *
4376 * <p>Notes:
4377 * <ol>
4378 *
4379 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
4380 * convenient way between the two arguments. For example,
4381 * JD(TT)=2450123.7 could be expressed in any of these ways,
4382 * among others:
4383 *<pre>
4384 * date1 date2
4385 *
4386 * 2450123.7 0.0 (JD method)
4387 * 2451545.0 -1421.3 (J2000 method)
4388 * 2400000.5 50123.2 (MJD method)
4389 * 2450123.5 0.2 (date & time method)
4390 *</pre>
4391 * The JD method is the most natural and convenient to use in
4392 * cases where the loss of several decimal digits of resolution
4393 * is acceptable. The J2000 method is best matched to the way
4394 * the argument is handled internally and will deliver the
4395 * optimum resolution. The MJD method and the date & time methods
4396 * are both good compromises between resolution and convenience.
4397 *
4398 * <li> The result, which is in radians, operates in the following sense:
4399 *
4400 * Greenwich apparent ST = GMST + equation of the equinoxes
4401 *</ol>
4402 *<p>Called:<ul>
4403 * <li>{@link #jauAnpm} normalize angle into range +/- pi
4404 * <li>{@link #jauGst06a} Greenwich apparent sidereal time, IAU 2006/2000A
4405 * <li>{@link #jauGmst06} Greenwich mean sidereal time, IAU 2006
4406 * </ul>
4407 *<p>Reference:
4408 *
4409 * <p>McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
4410 * IERS Technical Note No. 32, BKG
4411 *
4412 *@version 2008 May 18
4413 *
4414 * @since Release 20101201
4415 *
4416 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
4417 */
4418 public static double jauEe06a(double date1, double date2)
4419 {
4420 double gst06a, gmst06, ee;
4421
4422
4423 /* Apparent and mean sidereal times. */
4424 gst06a = jauGst06a(0.0, 0.0, date1, date2);
4425 gmst06 = jauGmst06(0.0, 0.0, date1, date2);
4426
4427 /* Equation of the equinoxes. */
4428 ee = jauAnpm(gst06a - gmst06);
4429
4430 return ee;
4431
4432 }
4433
4434 private static class TERM {
4435 final int nfa[]; /* coefficients of l,l',F,D,Om,LVe,LE,pA */
4436 final double s, c; /* sine and cosine coefficients */
4437 public TERM(int nfa[], double s, double c) {
4438 this.nfa = nfa;
4439 this.s = s;
4440 this.c = c;
4441 }
4442
4443 }
4444
4445
4446 /**
4447 * Equation of the equinoxes complementary terms, consistent with
4448 * IAU 2000 resolutions.
4449 *
4450 *<p>This function is derived from the International Astronomical Union's
4451 * SOFA (Standards Of Fundamental Astronomy) software collection.
4452 *
4453 *<p>Status: canonical model.
4454 *
4455 *<!-- Given: -->
4456 * @param date1 double TT as a 2-part Julian Date (Note 1)
4457 * @param date2 double TT as a 2-part Julian Date (Note 1)
4458 *
4459 * <!-- Returned (function value): -->
4460 * @return double complementary terms (Note 2)
4461 *
4462 * <p>Notes:
4463 * <ol>
4464 *
4465 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
4466 * convenient way between the two arguments. For example,
4467 * JD(TT)=2450123.7 could be expressed in any of these ways,
4468 * among others:
4469 *<pre>
4470 * date1 date2
4471 *
4472 * 2450123.7 0.0 (JD method)
4473 * 2451545.0 -1421.3 (J2000 method)
4474 * 2400000.5 50123.2 (MJD method)
4475 * 2450123.5 0.2 (date & time method)
4476 *</pre>
4477 * The JD method is the most natural and convenient to use in
4478 * cases where the loss of several decimal digits of resolution
4479 * is acceptable. The J2000 method is best matched to the way
4480 * the argument is handled internally and will deliver the
4481 * optimum resolution. The MJD method and the date & time methods
4482 * are both good compromises between resolution and convenience.
4483 *
4484 * <li> The "complementary terms" are part of the equation of the
4485 * equinoxes (EE), classically the difference between apparent and
4486 * mean Sidereal Time:
4487 *
4488 * GAST = GMST + EE
4489 *
4490 * with:
4491 *
4492 * EE = dpsi * cos(eps)
4493 *
4494 * where dpsi is the nutation in longitude and eps is the obliquity
4495 * of date. However, if the rotation of the Earth were constant in
4496 * an inertial frame the classical formulation would lead to
4497 * apparent irregularities in the UT1 timescale traceable to side-
4498 * effects of precession-nutation. In order to eliminate these
4499 * effects from UT1, "complementary terms" were introduced in 1994
4500 * (IAU, 1994) and took effect from 1997 (Capitaine and Gontier,
4501 * <li>:
4502 *
4503 * GAST = GMST + CT + EE
4504 *
4505 * By convention, the complementary terms are included as part of
4506 * the equation of the equinoxes rather than as part of the mean
4507 * Sidereal Time. This slightly compromises the "geometrical"
4508 * interpretation of mean sidereal time but is otherwise
4509 * inconsequential.
4510 *
4511 * The present function computes CT in the above expression,
4512 * compatible with IAU 2000 resolutions (Capitaine et al., 2002, and
4513 * IERS Conventions 2003).
4514 *</ol>
4515 *<p>Called:<ul>
4516 * <li>{@link #jauFal03} mean anomaly of the Moon
4517 * <li>{@link #jauFalp03} mean anomaly of the Sun
4518 * <li>{@link #jauFaf03} mean argument of the latitude of the Moon
4519 * <li>{@link #jauFad03} mean elongation of the Moon from the Sun
4520 * <li>{@link #jauFaom03} mean longitude of the Moon's ascending node
4521 * <li>{@link #jauFave03} mean longitude of Venus
4522 * <li>{@link #jauFae03} mean longitude of Earth
4523 * <li>{@link #jauFapa03} general accumulated precession in longitude
4524 * </ul>
4525 *<p>References:
4526 *
4527 * <p>Capitaine, N. & Gontier, A.-M., Astron. Astrophys., 275,
4528 * 645-650 (1993)
4529 *
4530 * <p>Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
4531 * implement the IAU 2000 definition of UT1", Astronomy &
4532 * Astrophysics, 406, 1135-1149 (2003)
4533 *
4534 * <p>IAU Resolution C7, Recommendation 3 (1994)
4535 *
4536 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
4537 * IERS Technical Note No. 32, BKG (2004)
4538 *
4539 *@version 2009 December 17
4540 *
4541 * @since Release 20101201
4542 *
4543 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
4544 */
4545 public static double jauEect00(double date1, double date2)
4546 {
4547 /* Time since J2000.0, in Julian centuries */
4548 double t;
4549
4550 /* Miscellaneous */
4551 int i, j;
4552 double a, s0, s1;
4553
4554 /* Fundamental arguments */
4555 double fa[] = new double[14];
4556
4557 /* Returned value. */
4558 double eect;
4559
4560 /* ----------------------------------------- */
4561 /* The series for the EE complementary terms */
4562 /* ----------------------------------------- */
4563
4564
4565 /* Terms of order t^0 */
4566 final TERM e0[] = {
4567
4568 /* 1-10 */
4569 new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, 2640.96e-6, -0.39e-6 ),
4570 new TERM(new int[]{ 0, 0, 0, 0, 2, 0, 0, 0}, 63.52e-6, -0.02e-6 ),
4571 new TERM(new int[]{ 0, 0, 2, -2, 3, 0, 0, 0}, 11.75e-6, 0.01e-6 ),
4572 new TERM(new int[]{ 0, 0, 2, -2, 1, 0, 0, 0}, 11.21e-6, 0.01e-6 ),
4573 new TERM(new int[]{ 0, 0, 2, -2, 2, 0, 0, 0}, -4.55e-6, 0.00e-6 ),
4574 new TERM(new int[]{ 0, 0, 2, 0, 3, 0, 0, 0}, 2.02e-6, 0.00e-6 ),
4575 new TERM(new int[]{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.98e-6, 0.00e-6 ),
4576 new TERM(new int[]{ 0, 0, 0, 0, 3, 0, 0, 0}, -1.72e-6, 0.00e-6 ),
4577 new TERM(new int[]{ 0, 1, 0, 0, 1, 0, 0, 0}, -1.41e-6, -0.01e-6 ),
4578 new TERM(new int[]{ 0, 1, 0, 0, -1, 0, 0, 0}, -1.26e-6, -0.01e-6 ),
4579
4580 /* 11-20 */
4581 new TERM(new int[]{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.63e-6, 0.00e-6 ),
4582 new TERM(new int[]{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.63e-6, 0.00e-6 ),
4583 new TERM(new int[]{ 0, 1, 2, -2, 3, 0, 0, 0}, 0.46e-6, 0.00e-6 ),
4584 new TERM(new int[]{ 0, 1, 2, -2, 1, 0, 0, 0}, 0.45e-6, 0.00e-6 ),
4585 new TERM(new int[]{ 0, 0, 4, -4, 4, 0, 0, 0}, 0.36e-6, 0.00e-6 ),
4586 new TERM(new int[]{ 0, 0, 1, -1, 1, -8, 12, 0}, -0.24e-6, -0.12e-6 ),
4587 new TERM(new int[]{ 0, 0, 2, 0, 0, 0, 0, 0}, 0.32e-6, 0.00e-6 ),
4588 new TERM(new int[]{ 0, 0, 2, 0, 2, 0, 0, 0}, 0.28e-6, 0.00e-6 ),
4589 new TERM(new int[]{ 1, 0, 2, 0, 3, 0, 0, 0}, 0.27e-6, 0.00e-6 ),
4590 new TERM(new int[]{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.26e-6, 0.00e-6 ),
4591
4592 /* 21-30 */
4593 new TERM(new int[]{ 0, 0, 2, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 ),
4594 new TERM(new int[]{ 0, 1, -2, 2, -3, 0, 0, 0}, 0.19e-6, 0.00e-6 ),
4595 new TERM(new int[]{ 0, 1, -2, 2, -1, 0, 0, 0}, 0.18e-6, 0.00e-6 ),
4596 new TERM(new int[]{ 0, 0, 0, 0, 0, 8,-13, -1}, -0.10e-6, 0.05e-6 ),
4597 new TERM(new int[]{ 0, 0, 0, 2, 0, 0, 0, 0}, 0.15e-6, 0.00e-6 ),
4598 new TERM(new int[]{ 2, 0, -2, 0, -1, 0, 0, 0}, -0.14e-6, 0.00e-6 ),
4599 new TERM(new int[]{ 1, 0, 0, -2, 1, 0, 0, 0}, 0.14e-6, 0.00e-6 ),
4600 new TERM(new int[]{ 0, 1, 2, -2, 2, 0, 0, 0}, -0.14e-6, 0.00e-6 ),
4601 new TERM(new int[]{ 1, 0, 0, -2, -1, 0, 0, 0}, 0.14e-6, 0.00e-6 ),
4602 new TERM(new int[]{ 0, 0, 4, -2, 4, 0, 0, 0}, 0.13e-6, 0.00e-6 ),
4603
4604 /* 31-33 */
4605 new TERM(new int[]{ 0, 0, 2, -2, 4, 0, 0, 0}, -0.11e-6, 0.00e-6 ),
4606 new TERM(new int[]{ 1, 0, -2, 0, -3, 0, 0, 0}, 0.11e-6, 0.00e-6 ),
4607 new TERM(new int[]{ 1, 0, -2, 0, -1, 0, 0, 0}, 0.11e-6, 0.00e-6 )
4608 };
4609
4610 /* Terms of order t^1 */
4611 final TERM e1[] = {
4612 new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.87e-6, 0.00e-6 )
4613 };
4614
4615 /* Number of terms in the series */
4616 final int NE0 = e0.length;
4617 final int NE1 = e1.length;
4618
4619 /*--------------------------------------------------------------------*/
4620
4621 /* Interval between fundamental epoch J2000.0 and current date (JC). */
4622 t = ((date1 - DJ00) + date2) / DJC;
4623
4624 /* Fundamental Arguments (from IERS Conventions 2003) */
4625
4626 /* Mean anomaly of the Moon. */
4627 fa[0] = jauFal03(t);
4628
4629 /* Mean anomaly of the Sun. */
4630 fa[1] = jauFalp03(t);
4631
4632 /* Mean longitude of the Moon minus that of the ascending node. */
4633 fa[2] = jauFaf03(t);
4634
4635 /* Mean elongation of the Moon from the Sun. */
4636 fa[3] = jauFad03(t);
4637
4638 /* Mean longitude of the ascending node of the Moon. */
4639 fa[4] = jauFaom03(t);
4640
4641 /* Mean longitude of Venus. */
4642 fa[5] = jauFave03(t);
4643
4644 /* Mean longitude of Earth. */
4645 fa[6] = jauFae03(t);
4646
4647 /* General precession in longitude. */
4648 fa[7] = jauFapa03(t);
4649
4650 /* Evaluate the EE complementary terms. */
4651 s0 = 0.0;
4652 s1 = 0.0;
4653
4654 for (i = NE0-1; i >= 0; i--) {
4655 a = 0.0;
4656 for (j = 0; j < 8; j++) {
4657 a += (double)(e0[i].nfa[j]) * fa[j];
4658 }
4659 s0 += e0[i].s * sin(a) + e0[i].c * cos(a);
4660 }
4661
4662 for (i = NE1-1; i >= 0; i--) {
4663 a = 0.0;
4664 for (j = 0; j < 8; j++) {
4665 a += (double)(e1[i].nfa[j]) * fa[j];
4666 }
4667 s1 += e1[i].s * sin(a) + e1[i].c * cos(a);
4668 }
4669
4670 eect = (s0 + s1 * t ) * DAS2R;
4671
4672 return eect;
4673
4674 }
4675
4676 /**
4677 * Reference Ellipsoid of Earth.
4678 *
4679 * The ellipsoid parameters are returned in the form of equatorial
4680 * radius in meters (a) and flattening (f). The latter is a number
4681 * around 0.00335, i.e. around 1/298.
4682 *
4683 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 1 Feb 2010
4684 *
4685 * @since AIDA Stage 1
4686 */
4687 public static class ReferenceEllipsoid{
4688 /** equatorial radius (meters, Note 2) */
4689 public double a;
4690 /** flattening (Note 2) */
4691 public double f ;
4692 public ReferenceEllipsoid(double a, double f ) {
4693 this.a = a;
4694 this.f = f;
4695 }
4696 }
4697 /**
4698 * Earth reference ellipsoids.
4699 *
4700 *<p>This function is derived from the International Astronomical Union's
4701 * JSOFA (Standards of Fundamental Astronomy) software collection.
4702 *
4703 *<p>Status: canonical.
4704 *
4705 *<!-- Given: -->
4706 * @param n int ellipsoid identifier (Note 1)
4707 *
4708 *<!-- Returned: -->
4709 * @return a double <u>returned</u> equatorial radius (meters, Note 2)
4710 * f double <u>returned</u> flattening (Note 2)
4711 *
4712 * <!-- Returned (function value): -->
4713 * @throws JSOFAIllegalParameter
4714 * int status:
4715 * 0 = OK
4716 * -1 = illegal identifier (Note 3)
4717 *
4718 * <p>Notes:
4719 * <ol>
4720 *
4721 * <li> The identifier n is a number that specifies the choice of
4722 * reference ellipsoid. The following are supported:
4723 *
4724 * n ellipsoid
4725 *
4726 * 1 WGS84
4727 * 2 GRS80
4728 * 3 WGS72
4729 *
4730 * The number n has no significance outside the JSOFA software.
4731 *
4732 * <li> The ellipsoid parameters are returned in the form of equatorial
4733 * radius in meters (a) and flattening (f). The latter is a number
4734 * around 0.00335, i.e. around 1/298.
4735 *
4736 * <li> For the case where an unsupported n value is supplied, zero a and
4737 * f are returned, as well as error status.
4738 *</ol>
4739 *<p>References:
4740 *
4741 * <p>Department of Defense World Geodetic System 1984, National
4742 * Imagery and Mapping Agency Technical Report 8350.2, Third
4743 * Edition, p3-2.
4744 *
4745 * <p>Moritz, H., Bull. Geodesique 66-2, 187 (1992).
4746 *
4747 * <p>The Department of Defense World Geodetic System 1972, World
4748 * Geodetic System Committee, May 1974.
4749 *
4750 * <p>Explanatory Supplement to the Astronomical Almanac,
4751 * P. Kenneth Seidelmann (ed), University Science Books (1992),
4752 * p220.
4753 *
4754 *@version 2010 January 18
4755 *
4756 * @since Release 20101201
4757 *
4758 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
4759 */
4760 public static ReferenceEllipsoid jauEform ( int n ) throws JSOFAIllegalParameter
4761 {
4762 double a,f;
4763 /* Look up a and f for the specified reference ellipsoid. */
4764 switch ( n ) {
4765 case 1:
4766
4767 /* WGS84. */
4768 a = 6378137.0;
4769 f = 1.0 / 298.257223563;
4770 break;
4771
4772 case 2:
4773
4774 /* GRS80. */
4775 a = 6378137.0;
4776 f = 1.0 / 298.257222101;
4777 break;
4778
4779 case 3:
4780
4781 /* WGS72. */
4782 a = 6378135.0;
4783 f = 1.0 / 298.26;
4784 break;
4785
4786 default:
4787
4788 /* Invalid identifier. */
4789 a = 0.0;
4790 f = 0.0;
4791 throw new JSOFAIllegalParameter("illegal ellipsoid identifier", -1);
4792
4793 }
4794
4795 /* OK status. */
4796 return new ReferenceEllipsoid(a, f);
4797
4798
4799 }
4800
4801
4802 /**
4803 * Equation of the origins, IAU 2006 precession and IAU 2000A nutation.
4804 *
4805 *<p>This function is derived from the International Astronomical Union's
4806 * SOFA (Standards Of Fundamental Astronomy) software collection.
4807 *
4808 *<p>Status: support function.
4809 *
4810 *<!-- Given: -->
4811 * @param date1 double TT as a 2-part Julian Date (Note 1)
4812 * @param date2 double TT as a 2-part Julian Date (Note 1)
4813 *
4814 * <!-- Returned (function value): -->
4815 * @return double equation of the origins in radians
4816 *
4817 * <p>Notes:
4818 * <ol>
4819 *
4820 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
4821 * convenient way between the two arguments. For example,
4822 * JD(TT)=2450123.7 could be expressed in any of these ways,
4823 * among others:
4824 *<pre>
4825 * date1 date2
4826 *
4827 * 2450123.7 0.0 (JD method)
4828 * 2451545.0 -1421.3 (J2000 method)
4829 * 2400000.5 50123.2 (MJD method)
4830 * 2450123.5 0.2 (date & time method)
4831 *</pre>
4832 * The JD method is the most natural and convenient to use in
4833 * cases where the loss of several decimal digits of resolution
4834 * is acceptable. The J2000 method is best matched to the way
4835 * the argument is handled internally and will deliver the
4836 * optimum resolution. The MJD method and the date & time methods
4837 * are both good compromises between resolution and convenience.
4838 *
4839 * <li> The equation of the origins is the distance between the true
4840 * equinox and the celestial intermediate origin and, equivalently,
4841 * the difference between Earth rotation angle and Greenwich
4842 * apparent sidereal time (ERA-GST). It comprises the precession
4843 * (since J2000.0) in right ascension plus the equation of the
4844 * equinoxes (including the small correction terms).
4845 *</ol>
4846 *<p>Called:<ul>
4847 * <li>{@link #jauPnm06a} classical NPB matrix, IAU 2006/2000A
4848 * <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
4849 * <li>{@link #jauS06} the CIO locator s, given X,Y, IAU 2006
4850 * <li>{@link #jauEors} equation of the origins, Given NPB matrix and s
4851 * </ul>
4852 *<p>References:
4853 *
4854 * <p>Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
4855 *
4856 * <p>Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
4857 *
4858 *@version 2008 May 16
4859 *
4860 * @since Release 20101201
4861 *
4862 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
4863 */
4864 public static double jauEo06a(double date1, double date2)
4865 {
4866 double r[][], s, eo;
4867
4868
4869 /* Classical nutation x precession x bias matrix. */
4870 r = jauPnm06a(date1, date2);
4871
4872 /* Extract CIP coordinates. */
4873 CelestialIntermediatePole cip = jauBpn2xy(r);
4874
4875 /* The CIO locator, s. */
4876 s = jauS06(date1, date2, cip.x, cip.y);
4877
4878 /* Solve for the EO. */
4879 eo = jauEors(r, s);
4880
4881 return eo;
4882
4883 }
4884
4885
4886 /**
4887 * Equation of the origins, given the classical NPB matrix and the
4888 * quantity s.
4889 *
4890 *<p>This function is derived from the International Astronomical Union's
4891 * SOFA (Standards Of Fundamental Astronomy) software collection.
4892 *
4893 *<p>Status: support function.
4894 *
4895 *<!-- Given: -->
4896 * @param rnpb double[3][3] classical nutation x precession x bias matrix
4897 * @param s double the quantity s (the CIO locator)
4898 *
4899 * <!-- Returned (function value): -->
4900 * @return double the equation of the origins in radians.
4901 *
4902 * <p>Notes:
4903 * <ol>
4904 *
4905 * <li> The equation of the origins is the distance between the true
4906 * equinox and the celestial intermediate origin and, equivalently,
4907 * the difference between Earth rotation angle and Greenwich
4908 * apparent sidereal time (ERA-GST). It comprises the precession
4909 * (since J2000.0) in right ascension plus the equation of the
4910 * equinoxes (including the small correction terms).
4911 *
4912 * <li> The algorithm is from Wallace & Capitaine (2006).
4913 *</ol>
4914 * References:
4915 *
4916 * <p>Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
4917 *
4918 * <p>Wallace, P. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
4919 *
4920 *@version 2008 May 26
4921 *
4922 * @since Release 20101201
4923 *
4924 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
4925 */
4926 public static double jauEors(double rnpb[][], double s)
4927 {
4928 double x, ax, xs, ys, zs, p, q, eo;
4929
4930
4931 /* Evaluate Wallace & Capitaine (2006) expression (16). */
4932 x = rnpb[2][0];
4933 ax = x / (1.0 + rnpb[2][2]);
4934 xs = 1.0 - ax * x;
4935 ys = -ax * rnpb[2][1];
4936 zs = -x;
4937 p = rnpb[0][0] * xs + rnpb[0][1] * ys + rnpb[0][2] * zs;
4938 q = rnpb[1][0] * xs + rnpb[1][1] * ys + rnpb[1][2] * zs;
4939 eo = ((p != 0) || (q != 0)) ? s - atan2(q, p) : s;
4940
4941 return eo;
4942
4943 }
4944
4945
4946 /**
4947 * Julian Date to Besselian Epoch.
4948 *
4949 *<p>This function is derived from the International Astronomical Union's
4950 * SOFA (Standards Of Fundamental Astronomy) software collection.
4951 *
4952 *<p>Status: support function.
4953 *
4954 *<!-- Given: -->
4955 * @param dj1 double Julian Date (see note)
4956 * @param dj2 double Julian Date (see note)
4957 *
4958 * <!-- Returned (function value): -->
4959 * @return double Besselian Epoch.
4960 *
4961 * Note:
4962 *
4963 * The Julian Date is supplied in two pieces, in the usual JSOFA
4964 * manner, which is designed to preserve time resolution. The
4965 * Julian Date is available as a single number by adding dj1 and
4966 * dj2. The maximum resolution is achieved if dj1 is 2451545D0
4967 * (J2000.0).
4968 *
4969 *<p>Reference:
4970 *
4971 * Lieske,J.H., 1979. Astron.Astrophys.,73,282.
4972 *
4973 *@version 2009 December 16
4974 *
4975 * @since Release 20101201
4976 *
4977 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
4978 */
4979 public static double jauEpb(double dj1, double dj2)
4980 {
4981 /* J2000.0 minus B1900.0 (2415019.81352) in Julian days */
4982 final double D1900 = 36524.68648;
4983
4984 return 1900.0 + ((dj1 - DJ00) + (dj2 + D1900)) / DTY;
4985
4986 }
4987
4988 /**
4989 * Besselian Epoch to Julian Date.
4990 *
4991 *<p>This function is derived from the International Astronomical Union's
4992 * SOFA (Standards Of Fundamental Astronomy) software collection.
4993 *
4994 *<p>Status: support function.
4995 *
4996 *<!-- Given: -->
4997 * @param epb double Besselian Epoch (e.g. 1957.3D0)
4998 *
4999 *<!-- Returned: -->
5000 * @return MJD zero-point: always 2400000.5 Modified Julian Date
5001 *
5002 * Note:
5003 *
5004 * The Julian Date is returned in two pieces, in the usual JSOFA
5005 * manner, which is designed to preserve time resolution. The
5006 * Julian Date is available as a single number by adding djm0 and
5007 * djm.
5008 *
5009 *<p>Reference:
5010 *
5011 * <p>Lieske, J.H., 1979, Astron.Astrophys. 73, 282.
5012 *
5013 *@version 2008 May 24
5014 *
5015 * @since Release 20101201
5016 *
5017 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
5018 */
5019 public static JulianDate jauEpb2jd(double epb)
5020 {
5021 double djm0, djm;
5022 djm0 = 2400000.5;
5023 djm = 15019.81352 + (epb - 1900.0) * DTY;
5024
5025 return new JulianDate(djm0, djm);
5026
5027 }
5028
5029
5030 /**
5031 * Julian Date to Julian Epoch.
5032 *
5033 *<p>This function is derived from the International Astronomical Union's
5034 * SOFA (Standards Of Fundamental Astronomy) software collection.
5035 *
5036 *<p>Status: support function.
5037 *
5038 *<!-- Given: -->
5039 * @param dj1 double Julian Date (see note)
5040 * @param dj2 double Julian Date (see note)
5041 *
5042 * <!-- Returned (function value): -->
5043 * @return double Julian Epoch
5044 *
5045 * Note:
5046 *
5047 * The Julian Date is supplied in two pieces, in the usual JSOFA
5048 * manner, which is designed to preserve time resolution. The
5049 * Julian Date is available as a single number by adding dj1 and
5050 * dj2. The maximum resolution is achieved if dj1 is 2451545D0
5051 * (J2000.0).
5052 *
5053 *<p>Reference:
5054 *
5055 * <p>Lieske, J.H., 1979, Astron.Astrophys. 73, 282.
5056 *
5057 *@version 2009 December 16
5058 *
5059 * @since Release 20101201
5060 *
5061 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
5062 */
5063 public static double jauEpj(double dj1, double dj2)
5064 {
5065 return 2000.0 + ((dj1 - DJ00) + dj2) / DJY;
5066
5067 }
5068
5069
5070 /**
5071 * Julian Epoch to Julian Date.
5072 *
5073 *<p>This function is derived from the International Astronomical Union's
5074 * SOFA (Standards Of Fundamental Astronomy) software collection.
5075 *
5076 *<p>Status: support function.
5077 *
5078 *<!-- Given: -->
5079 * @param epj double Julian Epoch (e.g. 1996.8D0)
5080 *
5081 *<!-- Returned: -->
5082 * @return MJD zero-point: always 2400000.5 Modified Julian Date
5083 *
5084 * Note:
5085 *
5086 * The Julian Date is returned in two pieces, in the usual JSOFA
5087 * manner, which is designed to preserve time resolution. The
5088 * Julian Date is available as a single number by adding djm0 and
5089 * djm.
5090 *
5091 *<p>Reference:
5092 *
5093 * <p>Lieske, J.H., 1979, Astron.Astrophys. 73, 282.
5094 *
5095 *@version 2008 May 11
5096 *
5097 * @since Release 20101201
5098 *
5099 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
5100 */
5101 public static JulianDate jauEpj2jd(double epj)
5102 {
5103 double djm0, djm;
5104 djm0 = 2400000.5;
5105 djm = 51544.5 + (epj - 2000.0) * 365.25;
5106
5107 return new JulianDate(djm0, djm);
5108
5109 }
5110
5111
5112 /*
5113 * A utility class to get round 65536 byte limit on functions in java - The static initializer is too large on its own. - So split into two classes for no real semantic reason
5114 */
5115 static private final class Ephemeris extends SSB {
5116
5117
5118 /**
5119 * ----------------------
5120 * Ephemeris Coefficients
5121 * ----------------------
5122 *
5123 * The ephemeris consists of harmonic terms for predicting (i) the Sun
5124 * to Earth vector and (ii) the Solar-System-barycenter to Sun vector
5125 * respectively. The coefficients are stored in arrays which, although
5126 * 1-demensional, contain groups of three. Each triplet of
5127 * coefficients is the amplitude, phase and frequency for one term in
5128 * the model, and each array contains the number of terms called for by
5129 * the model.
5130 *
5131 * There are eighteen such arrays, named as follows:
5132 *<pre>
5133 * array model power of T component
5134 *
5135 * e0x Sun-to-Earth 0 x
5136 * e0y Sun-to-Earth 0 y
5137 * e0z Sun-to-Earth 0 z
5138 *
5139 * e1x Sun-to-Earth 1 x
5140 * e1y Sun-to-Earth 1 y
5141 * e1z Sun-to-Earth 1 z
5142 *
5143 * e2x Sun-to-Earth 2 x
5144 * e2y Sun-to-Earth 2 y
5145 * e2z Sun-to-Earth 2 z
5146 *
5147 * s0x SSB-to-Sun 0 x
5148 * s0y SSB-to-Sun 0 y
5149 * s0z SSB-to-Sun 0 z
5150 *
5151 * s1x SSB-to-Sun 1 x
5152 * s1y SSB-to-Sun 1 y
5153 * s1z SSB-to-Sun 1 z
5154 *
5155 * s2x SSB-to-Sun 2 x
5156 * s2y SSB-to-Sun 2 y
5157 * s2z SSB-to-Sun 2 z
5158 *<pre>
5159 */
5160
5161 /* Sun-to-Earth, T^0, X */
5162 static final double e0x[] = {
5163 0.9998292878132e+00, 0.1753485171504e+01, 0.6283075850446e+01,
5164 0.8352579567414e-02, 0.1710344404582e+01, 0.1256615170089e+02,
5165 0.5611445335148e-02, 0.0000000000000e+00, 0.0000000000000e+00,
5166 0.1046664295572e-03, 0.1667225416770e+01, 0.1884922755134e+02,
5167 0.3110842534677e-04, 0.6687513390251e+00, 0.8399684731857e+02,
5168 0.2552413503550e-04, 0.5830637358413e+00, 0.5296909721118e+00,
5169 0.2137207845781e-04, 0.1092330954011e+01, 0.1577343543434e+01,
5170 0.1680240182951e-04, 0.4955366134987e+00, 0.6279552690824e+01,
5171 0.1679012370795e-04, 0.6153014091901e+01, 0.6286599010068e+01,
5172 0.1445526946777e-04, 0.3472744100492e+01, 0.2352866153506e+01,
5173
5174 0.1091038246184e-04, 0.3689845786119e+01, 0.5223693906222e+01,
5175 0.9344399733932e-05, 0.6073934645672e+01, 0.1203646072878e+02,
5176 0.8993182910652e-05, 0.3175705249069e+01, 0.1021328554739e+02,
5177 0.5665546034116e-05, 0.2152484672246e+01, 0.1059381944224e+01,
5178 0.6844146703035e-05, 0.1306964099750e+01, 0.5753384878334e+01,
5179 0.7346610905565e-05, 0.4354980070466e+01, 0.3981490189893e+00,
5180 0.6815396474414e-05, 0.2218229211267e+01, 0.4705732307012e+01,
5181 0.6112787253053e-05, 0.5384788425458e+01, 0.6812766822558e+01,
5182 0.4518120711239e-05, 0.6087604012291e+01, 0.5884926831456e+01,
5183 0.4521963430706e-05, 0.1279424524906e+01, 0.6256777527156e+01,
5184
5185 0.4497426764085e-05, 0.5369129144266e+01, 0.6309374173736e+01,
5186 0.4062190566959e-05, 0.5436473303367e+00, 0.6681224869435e+01,
5187 0.5412193480192e-05, 0.7867838528395e+00, 0.7755226100720e+00,
5188 0.5469839049386e-05, 0.1461440311134e+01, 0.1414349524433e+02,
5189 0.5205264083477e-05, 0.4432944696116e+01, 0.7860419393880e+01,
5190 0.2149759935455e-05, 0.4502237496846e+01, 0.1150676975667e+02,
5191 0.2279109618501e-05, 0.1239441308815e+01, 0.7058598460518e+01,
5192 0.2259282939683e-05, 0.3272430985331e+01, 0.4694002934110e+01,
5193 0.2558950271319e-05, 0.2265471086404e+01, 0.1216800268190e+02,
5194 0.2561581447555e-05, 0.1454740653245e+01, 0.7099330490126e+00,
5195
5196 0.1781441115440e-05, 0.2962068630206e+01, 0.7962980379786e+00,
5197 0.1612005874644e-05, 0.1473255041006e+01, 0.5486777812467e+01,
5198 0.1818630667105e-05, 0.3743903293447e+00, 0.6283008715021e+01,
5199 0.1818601377529e-05, 0.6274174354554e+01, 0.6283142985870e+01,
5200 0.1554475925257e-05, 0.1624110906816e+01, 0.2513230340178e+02,
5201 0.2090948029241e-05, 0.5852052276256e+01, 0.1179062909082e+02,
5202 0.2000176345460e-05, 0.4072093298513e+01, 0.1778984560711e+02,
5203 0.1289535917759e-05, 0.5217019331069e+01, 0.7079373888424e+01,
5204 0.1281135307881e-05, 0.4802054538934e+01, 0.3738761453707e+01,
5205 0.1518229005692e-05, 0.8691914742502e+00, 0.2132990797783e+00,
5206
5207 0.9450128579027e-06, 0.4601859529950e+01, 0.1097707878456e+02,
5208 0.7781119494996e-06, 0.1844352816694e+01, 0.8827390247185e+01,
5209 0.7733407759912e-06, 0.3582790154750e+01, 0.5507553240374e+01,
5210 0.7350644318120e-06, 0.2695277788230e+01, 0.1589072916335e+01,
5211 0.6535928827023e-06, 0.3651327986142e+01, 0.1176985366291e+02,
5212 0.6324624183656e-06, 0.2241302375862e+01, 0.6262300422539e+01,
5213 0.6298565300557e-06, 0.4407122406081e+01, 0.6303851278352e+01,
5214 0.8587037089179e-06, 0.3024307223119e+01, 0.1672837615881e+03,
5215 0.8299954491035e-06, 0.6192539428237e+01, 0.3340612434717e+01,
5216 0.6311263503401e-06, 0.2014758795416e+01, 0.7113454667900e-02,
5217
5218 0.6005646745452e-06, 0.3399500503397e+01, 0.4136910472696e+01,
5219 0.7917715109929e-06, 0.2493386877837e+01, 0.6069776770667e+01,
5220 0.7556958099685e-06, 0.4159491740143e+01, 0.6496374930224e+01,
5221 0.6773228244949e-06, 0.4034162934230e+01, 0.9437762937313e+01,
5222 0.5370708577847e-06, 0.1562219163734e+01, 0.1194447056968e+01,
5223 0.5710804266203e-06, 0.2662730803386e+01, 0.6282095334605e+01,
5224 0.5709824583726e-06, 0.3985828430833e+01, 0.6284056366286e+01,
5225 0.5143950896447e-06, 0.1308144688689e+01, 0.6290189305114e+01,
5226 0.5088010604546e-06, 0.5352817214804e+01, 0.6275962395778e+01,
5227 0.4960369085172e-06, 0.2644267922349e+01, 0.6127655567643e+01,
5228
5229 0.4803137891183e-06, 0.4008844192080e+01, 0.6438496133249e+01,
5230 0.5731747768225e-06, 0.3794550174597e+01, 0.3154687086868e+01,
5231 0.4735947960579e-06, 0.6107118308982e+01, 0.3128388763578e+01,
5232 0.4808348796625e-06, 0.4771458618163e+01, 0.8018209333619e+00,
5233 0.4115073743137e-06, 0.3327111335159e+01, 0.8429241228195e+01,
5234 0.5230575889287e-06, 0.5305708551694e+01, 0.1336797263425e+02,
5235 0.5133977889215e-06, 0.5784230738814e+01, 0.1235285262111e+02,
5236 0.5065815825327e-06, 0.2052064793679e+01, 0.1185621865188e+02,
5237 0.4339831593868e-06, 0.3644994195830e+01, 0.1726015463500e+02,
5238 0.3952928638953e-06, 0.4930376436758e+01, 0.5481254917084e+01,
5239
5240 0.4898498111942e-06, 0.4542084219731e+00, 0.9225539266174e+01,
5241 0.4757490209328e-06, 0.3161126388878e+01, 0.5856477690889e+01,
5242 0.4727701669749e-06, 0.6214993845446e+00, 0.2544314396739e+01,
5243 0.3800966681863e-06, 0.3040132339297e+01, 0.4265981595566e+00,
5244 0.3257301077939e-06, 0.8064977360087e+00, 0.3930209696940e+01,
5245 0.3255810528674e-06, 0.1974147981034e+01, 0.2146165377750e+01,
5246 0.3252029748187e-06, 0.2845924913135e+01, 0.4164311961999e+01,
5247 0.3255505635308e-06, 0.3017900824120e+01, 0.5088628793478e+01,
5248 0.2801345211990e-06, 0.6109717793179e+01, 0.1256967486051e+02,
5249 0.3688987740970e-06, 0.2911550235289e+01, 0.1807370494127e+02,
5250
5251 0.2475153429458e-06, 0.2179146025856e+01, 0.2629832328990e-01,
5252 0.3033457749150e-06, 0.1994161050744e+01, 0.4535059491685e+01,
5253 0.2186743763110e-06, 0.5125687237936e+01, 0.1137170464392e+02,
5254 0.2764777032774e-06, 0.4822646860252e+00, 0.1256262854127e+02,
5255 0.2199028768592e-06, 0.4637633293831e+01, 0.1255903824622e+02,
5256 0.2046482824760e-06, 0.1467038733093e+01, 0.7084896783808e+01,
5257 0.2611209147507e-06, 0.3044718783485e+00, 0.7143069561767e+02,
5258 0.2286079656818e-06, 0.4764220356805e+01, 0.8031092209206e+01,
5259 0.1855071202587e-06, 0.3383637774428e+01, 0.1748016358760e+01,
5260 0.2324669506784e-06, 0.6189088449251e+01, 0.1831953657923e+02,
5261
5262 0.1709528015688e-06, 0.5874966729774e+00, 0.4933208510675e+01,
5263 0.2168156875828e-06, 0.4302994009132e+01, 0.1044738781244e+02,
5264 0.2106675556535e-06, 0.3800475419891e+01, 0.7477522907414e+01,
5265 0.1430213830465e-06, 0.1294660846502e+01, 0.2942463415728e+01,
5266 0.1388396901944e-06, 0.4594797202114e+01, 0.8635942003952e+01,
5267 0.1922258844190e-06, 0.4943044543591e+00, 0.1729818233119e+02,
5268 0.1888460058292e-06, 0.2426943912028e+01, 0.1561374759853e+03,
5269 0.1789449386107e-06, 0.1582973303499e+00, 0.1592596075957e+01,
5270 0.1360803685374e-06, 0.5197240440504e+01, 0.1309584267300e+02,
5271 0.1504038014709e-06, 0.3120360916217e+01, 0.1649636139783e+02,
5272
5273 0.1382769533389e-06, 0.6164702888205e+01, 0.7632943190217e+01,
5274 0.1438059769079e-06, 0.1437423770979e+01, 0.2042657109477e+02,
5275 0.1326303260037e-06, 0.3609688799679e+01, 0.1213955354133e+02,
5276 0.1159244950540e-06, 0.5463018167225e+01, 0.5331357529664e+01,
5277 0.1433118149136e-06, 0.6028909912097e+01, 0.7342457794669e+01,
5278 0.1234623148594e-06, 0.3109645574997e+01, 0.6279485555400e+01,
5279 0.1233949875344e-06, 0.3539359332866e+01, 0.6286666145492e+01,
5280 0.9927196061299e-07, 0.1259321569772e+01, 0.7234794171227e+01,
5281 0.1242302191316e-06, 0.1065949392609e+01, 0.1511046609763e+02,
5282 0.1098402195201e-06, 0.2192508743837e+01, 0.1098880815746e+02,
5283
5284 0.1158191395315e-06, 0.4054411278650e+01, 0.5729506548653e+01,
5285 0.9048475596241e-07, 0.5429764748518e+01, 0.9623688285163e+01,
5286 0.8889853269023e-07, 0.5046586206575e+01, 0.6148010737701e+01,
5287 0.1048694242164e-06, 0.2628858030806e+01, 0.6836645152238e+01,
5288 0.1112308378646e-06, 0.4177292719907e+01, 0.1572083878776e+02,
5289 0.8631729709901e-07, 0.1601345232557e+01, 0.6418140963190e+01,
5290 0.8527816951664e-07, 0.2463888997513e+01, 0.1471231707864e+02,
5291 0.7892139456991e-07, 0.3154022088718e+01, 0.2118763888447e+01,
5292 0.1051782905236e-06, 0.4795035816088e+01, 0.1349867339771e+01,
5293 0.1048219943164e-06, 0.2952983395230e+01, 0.5999216516294e+01,
5294
5295 0.7435760775143e-07, 0.5420547991464e+01, 0.6040347114260e+01,
5296 0.9869574106949e-07, 0.3695646753667e+01, 0.6566935184597e+01,
5297 0.9156886364226e-07, 0.3922675306609e+01, 0.5643178611111e+01,
5298 0.7006834356188e-07, 0.1233968624861e+01, 0.6525804586632e+01,
5299 0.9806170182601e-07, 0.1919542280684e+01, 0.2122839202813e+02,
5300 0.9052289673607e-07, 0.4615902724369e+01, 0.4690479774488e+01,
5301 0.7554200867893e-07, 0.1236863719072e+01, 0.1253985337760e+02,
5302 0.8215741286498e-07, 0.3286800101559e+00, 0.1097355562493e+02,
5303 0.7185178575397e-07, 0.5880942158367e+01, 0.6245048154254e+01,
5304 0.7130726476180e-07, 0.7674871987661e+00, 0.6321103546637e+01,
5305
5306 0.6650894461162e-07, 0.6987129150116e+00, 0.5327476111629e+01,
5307 0.7396888823688e-07, 0.3576824794443e+01, 0.5368044267797e+00,
5308 0.7420588884775e-07, 0.5033615245369e+01, 0.2354323048545e+02,
5309 0.6141181642908e-07, 0.9449927045673e+00, 0.1296430071988e+02,
5310 0.6373557924058e-07, 0.6206342280341e+01, 0.9517183207817e+00,
5311 0.6359474329261e-07, 0.5036079095757e+01, 0.1990745094947e+01,
5312 0.5740173582646e-07, 0.6105106371350e+01, 0.9555997388169e+00,
5313 0.7019864084602e-07, 0.7237747359018e+00, 0.5225775174439e+00,
5314 0.6398054487042e-07, 0.3976367969666e+01, 0.2407292145756e+02,
5315 0.7797092650498e-07, 0.4305423910623e+01, 0.2200391463820e+02,
5316
5317 0.6466760000900e-07, 0.3500136825200e+01, 0.5230807360890e+01,
5318 0.7529417043890e-07, 0.3514779246100e+01, 0.1842262939178e+02,
5319 0.6924571140892e-07, 0.2743457928679e+01, 0.1554202828031e+00,
5320 0.6220798650222e-07, 0.2242598118209e+01, 0.1845107853235e+02,
5321 0.5870209391853e-07, 0.2332832707527e+01, 0.6398972393349e+00,
5322 0.6263953473888e-07, 0.2191105358956e+01, 0.6277552955062e+01,
5323 0.6257781390012e-07, 0.4457559396698e+01, 0.6288598745829e+01,
5324 0.5697304945123e-07, 0.3499234761404e+01, 0.1551045220144e+01,
5325 0.6335438746791e-07, 0.6441691079251e+00, 0.5216580451554e+01,
5326 0.6377258441152e-07, 0.2252599151092e+01, 0.5650292065779e+01,
5327
5328 0.6484841818165e-07, 0.1992812417646e+01, 0.1030928125552e+00,
5329 0.4735551485250e-07, 0.3744672082942e+01, 0.1431416805965e+02,
5330 0.4628595996170e-07, 0.1334226211745e+01, 0.5535693017924e+00,
5331 0.6258152336933e-07, 0.4395836159154e+01, 0.2608790314060e+02,
5332 0.6196171366594e-07, 0.2587043007997e+01, 0.8467247584405e+02,
5333 0.6159556952126e-07, 0.4782499769128e+01, 0.2394243902548e+03,
5334 0.4987741172394e-07, 0.7312257619924e+00, 0.7771377146812e+02,
5335 0.5459280703142e-07, 0.3001376372532e+01, 0.6179983037890e+01,
5336 0.4863461189999e-07, 0.3767222128541e+01, 0.9027992316901e+02,
5337 0.5349912093158e-07, 0.3663594450273e+01, 0.6386168663001e+01,
5338
5339 0.5673725607806e-07, 0.4331187919049e+01, 0.6915859635113e+01,
5340 0.4745485060512e-07, 0.5816195745518e+01, 0.6282970628506e+01,
5341 0.4745379005326e-07, 0.8323672435672e+00, 0.6283181072386e+01,
5342 0.4049002796321e-07, 0.3785023976293e+01, 0.6254626709878e+01,
5343 0.4247084014515e-07, 0.2378220728783e+01, 0.7875671926403e+01,
5344 0.4026912363055e-07, 0.2864103423269e+01, 0.6311524991013e+01,
5345 0.4062935011774e-07, 0.2415408595975e+01, 0.3634620989887e+01,
5346 0.5347771048509e-07, 0.3343479309801e+01, 0.2515860172507e+02,
5347 0.4829494136505e-07, 0.2821742398262e+01, 0.5760498333002e+01,
5348 0.4342554404599e-07, 0.5624662458712e+01, 0.7238675589263e+01,
5349
5350 0.4021599184361e-07, 0.5557250275009e+00, 0.1101510648075e+02,
5351 0.4104900474558e-07, 0.3296691780005e+01, 0.6709674010002e+01,
5352 0.4376532905131e-07, 0.3814443999443e+01, 0.6805653367890e+01,
5353 0.3314590480650e-07, 0.3560229189250e+01, 0.1259245002418e+02,
5354 0.3232421839643e-07, 0.5185389180568e+01, 0.1066495398892e+01,
5355 0.3541176318876e-07, 0.3921381909679e+01, 0.9917696840332e+01,
5356 0.3689831242681e-07, 0.4190658955386e+01, 0.1192625446156e+02,
5357 0.3890605376774e-07, 0.5546023371097e+01, 0.7478166569050e-01,
5358 0.3038559339780e-07, 0.6231032794494e+01, 0.1256621883632e+02,
5359 0.3137083969782e-07, 0.6207063419190e+01, 0.4292330755499e+01,
5360
5361 0.4024004081854e-07, 0.1195257375713e+01, 0.1334167431096e+02,
5362 0.3300234879283e-07, 0.1804694240998e+01, 0.1057540660594e+02,
5363 0.3635399155575e-07, 0.5597811343500e+01, 0.6208294184755e+01,
5364 0.3032668691356e-07, 0.3191059366530e+01, 0.1805292951336e+02,
5365 0.2809652069058e-07, 0.4094348032570e+01, 0.3523159621801e-02,
5366 0.3696955383823e-07, 0.5219282738794e+01, 0.5966683958112e+01,
5367 0.3562894142503e-07, 0.1037247544554e+01, 0.6357857516136e+01,
5368 0.3510598524148e-07, 0.1430020816116e+01, 0.6599467742779e+01,
5369 0.3617736142953e-07, 0.3002911403677e+01, 0.6019991944201e+01,
5370 0.2624524910730e-07, 0.2437046757292e+01, 0.6702560555334e+01,
5371
5372 0.2535824204490e-07, 0.1581594689647e+01, 0.3141537925223e+02,
5373 0.3519787226257e-07, 0.5379863121521e+01, 0.2505706758577e+03,
5374 0.2578406709982e-07, 0.4904222639329e+01, 0.1673046366289e+02,
5375 0.3423887981473e-07, 0.3646448997315e+01, 0.6546159756691e+01,
5376 0.2776083886467e-07, 0.3307829300144e+01, 0.1272157198369e+02,
5377 0.3379592818379e-07, 0.1747541251125e+01, 0.1494531617769e+02,
5378 0.3050255426284e-07, 0.1784689432607e-01, 0.4732030630302e+01,
5379 0.2652378350236e-07, 0.4420055276260e+01, 0.5863591145557e+01,
5380 0.2374498173768e-07, 0.3629773929208e+01, 0.2388894113936e+01,
5381 0.2716451255140e-07, 0.3079623706780e+01, 0.1202934727411e+02,
5382
5383 0.3038583699229e-07, 0.3312487903507e+00, 0.1256608456547e+02,
5384 0.2220681228760e-07, 0.5265520401774e+01, 0.1336244973887e+02,
5385 0.3044156540912e-07, 0.4766664081250e+01, 0.2908881142201e+02,
5386 0.2731859923561e-07, 0.5069146530691e+01, 0.1391601904066e+02,
5387 0.2285603018171e-07, 0.5954935112271e+01, 0.6076890225335e+01,
5388 0.2025006454555e-07, 0.4061789589267e+01, 0.4701116388778e+01,
5389 0.2012597519804e-07, 0.2485047705241e+01, 0.6262720680387e+01,
5390 0.2003406962258e-07, 0.4163779209320e+01, 0.6303431020504e+01,
5391 0.2207863441371e-07, 0.6923839133828e+00, 0.6489261475556e+01,
5392 0.2481374305624e-07, 0.5944173595676e+01, 0.1204357418345e+02,
5393
5394 0.2130923288870e-07, 0.4641013671967e+01, 0.5746271423666e+01,
5395 0.2446370543391e-07, 0.6125796518757e+01, 0.1495633313810e+00,
5396 0.1932492759052e-07, 0.2234572324504e+00, 0.1352175143971e+02,
5397 0.2600122568049e-07, 0.4281012405440e+01, 0.4590910121555e+01,
5398 0.2431754047488e-07, 0.1429943874870e+00, 0.1162474756779e+01,
5399 0.1875902869209e-07, 0.9781803816948e+00, 0.6279194432410e+01,
5400 0.1874381139426e-07, 0.5670368130173e+01, 0.6286957268481e+01,
5401 0.2156696047173e-07, 0.2008985006833e+01, 0.1813929450232e+02,
5402 0.1965076182484e-07, 0.2566186202453e+00, 0.4686889479442e+01,
5403 0.2334816372359e-07, 0.4408121891493e+01, 0.1002183730415e+02,
5404
5405 0.1869937408802e-07, 0.5272745038656e+01, 0.2427287361862e+00,
5406 0.2436236460883e-07, 0.4407720479029e+01, 0.9514313292143e+02,
5407 0.1761365216611e-07, 0.1943892315074e+00, 0.1351787002167e+02,
5408 0.2156289480503e-07, 0.1418570924545e+01, 0.6037244212485e+01,
5409 0.2164748979255e-07, 0.4724603439430e+01, 0.2301353951334e+02,
5410 0.2222286670853e-07, 0.2400266874598e+01, 0.1266924451345e+02,
5411 0.2070901414929e-07, 0.5230348028732e+01, 0.6528907488406e+01,
5412 0.1792745177020e-07, 0.2099190328945e+01, 0.6819880277225e+01,
5413 0.1841802068445e-07, 0.3467527844848e+00, 0.6514761976723e+02,
5414 0.1578401631718e-07, 0.7098642356340e+00, 0.2077542790660e-01,
5415
5416 0.1561690152531e-07, 0.5943349620372e+01, 0.6272439236156e+01,
5417 0.1558591045463e-07, 0.7040653478980e+00, 0.6293712464735e+01,
5418 0.1737356469576e-07, 0.4487064760345e+01, 0.1765478049437e+02,
5419 0.1434755619991e-07, 0.2993391570995e+01, 0.1102062672231e+00,
5420 0.1482187806654e-07, 0.2278049198251e+01, 0.1052268489556e+01,
5421 0.1424812827089e-07, 0.1682114725827e+01, 0.1311972100268e+02,
5422 0.1380282448623e-07, 0.3262668602579e+01, 0.1017725758696e+02,
5423 0.1811481244566e-07, 0.3187771221777e+01, 0.1887552587463e+02,
5424 0.1504446185696e-07, 0.5650162308647e+01, 0.7626583626240e-01,
5425 0.1740776154137e-07, 0.5487068607507e+01, 0.1965104848470e+02,
5426
5427 0.1374339536251e-07, 0.5745688172201e+01, 0.6016468784579e+01,
5428 0.1761377477704e-07, 0.5748060203659e+01, 0.2593412433514e+02,
5429 0.1535138225795e-07, 0.6226848505790e+01, 0.9411464614024e+01,
5430 0.1788140543676e-07, 0.6189318878563e+01, 0.3301902111895e+02,
5431 0.1375002807996e-07, 0.5371812884394e+01, 0.6327837846670e+00,
5432 0.1242115758632e-07, 0.1471687569712e+01, 0.3894181736510e+01,
5433 0.1450977333938e-07, 0.4143836662127e+01, 0.1277945078067e+02,
5434 0.1297579575023e-07, 0.9003477661957e+00, 0.6549682916313e+01,
5435 0.1462667934821e-07, 0.5760505536428e+01, 0.1863592847156e+02,
5436 0.1381774374799e-07, 0.1085471729463e+01, 0.2379164476796e+01,
5437
5438 0.1682333169307e-07, 0.5409870870133e+01, 0.1620077269078e+02,
5439 0.1190812918837e-07, 0.1397205174601e+01, 0.1149965630200e+02,
5440 0.1221434762106e-07, 0.9001804809095e+00, 0.1257326515556e+02,
5441 0.1549934644860e-07, 0.4262528275544e+01, 0.1820933031200e+02,
5442 0.1252138953050e-07, 0.1411642012027e+01, 0.6993008899458e+01,
5443 0.1237078905387e-07, 0.2844472403615e+01, 0.2435678079171e+02,
5444 0.1446953389615e-07, 0.5295835522223e+01, 0.3813291813120e-01,
5445 0.1388446457170e-07, 0.4969428135497e+01, 0.2458316379602e+00,
5446 0.1019339179228e-07, 0.2491369561806e+01, 0.6112403035119e+01,
5447 0.1258880815343e-07, 0.4679426248976e+01, 0.5429879531333e+01,
5448
5449 0.1297768238261e-07, 0.1074509953328e+01, 0.1249137003520e+02,
5450 0.9913505718094e-08, 0.4735097918224e+01, 0.6247047890016e+01,
5451 0.9830453155969e-08, 0.4158649187338e+01, 0.6453748665772e+01,
5452 0.1192615865309e-07, 0.3438208613699e+01, 0.6290122169689e+01,
5453 0.9835874798277e-08, 0.1913300781229e+01, 0.6319103810876e+01,
5454 0.9639087569277e-08, 0.9487683644125e+00, 0.8273820945392e+01,
5455 0.1175716107001e-07, 0.3228141664287e+01, 0.6276029531202e+01,
5456 0.1018926508678e-07, 0.2216607854300e+01, 0.1254537627298e+02,
5457 0.9500087869225e-08, 0.2625116459733e+01, 0.1256517118505e+02,
5458 0.9664192916575e-08, 0.5860562449214e+01, 0.6259197520765e+01,
5459
5460 0.9612858712203e-08, 0.7885682917381e+00, 0.6306954180126e+01,
5461 0.1117645675413e-07, 0.3932148831189e+01, 0.1779695906178e+02,
5462 0.1158864052160e-07, 0.9995605521691e+00, 0.1778273215245e+02,
5463 0.9021043467028e-08, 0.5263769742673e+01, 0.6172869583223e+01,
5464 0.8836134773563e-08, 0.1496843220365e+01, 0.1692165728891e+01,
5465 0.1045872200691e-07, 0.7009039517214e+00, 0.2204125344462e+00,
5466 0.1211463487798e-07, 0.4041544938511e+01, 0.8257698122054e+02,
5467 0.8541990804094e-08, 0.1447586692316e+01, 0.6393282117669e+01,
5468 0.1038720703636e-07, 0.4594249718112e+00, 0.1550861511662e+02,
5469 0.1126722351445e-07, 0.3925550579036e+01, 0.2061856251104e+00,
5470
5471 0.8697373859631e-08, 0.4411341856037e+01, 0.9491756770005e+00,
5472 0.8869380028441e-08, 0.2402659724813e+01, 0.3903911373650e+01,
5473 0.9247014693258e-08, 0.1401579743423e+01, 0.6267823317922e+01,
5474 0.9205062930950e-08, 0.5245978000814e+01, 0.6298328382969e+01,
5475 0.8000745038049e-08, 0.3590803356945e+01, 0.2648454860559e+01,
5476 0.9168973650819e-08, 0.2470150501679e+01, 0.1498544001348e+03,
5477 0.1075444949238e-07, 0.1328606161230e+01, 0.3694923081589e+02,
5478 0.7817298525817e-08, 0.6162256225998e+01, 0.4804209201333e+01,
5479 0.9541469226356e-08, 0.3942568967039e+01, 0.1256713221673e+02,
5480 0.9821910122027e-08, 0.2360246287233e+00, 0.1140367694411e+02,
5481
5482 0.9897822023777e-08, 0.4619805634280e+01, 0.2280573557157e+02,
5483 0.7737289283765e-08, 0.3784727847451e+01, 0.7834121070590e+01,
5484 0.9260204034710e-08, 0.2223352487601e+01, 0.2787043132925e+01,
5485 0.7320252888486e-08, 0.1288694636874e+01, 0.6282655592598e+01,
5486 0.7319785780946e-08, 0.5359869567774e+01, 0.6283496108294e+01,
5487 0.7147219933778e-08, 0.5516616675856e+01, 0.1725663147538e+02,
5488 0.7946502829878e-08, 0.2630459984567e+01, 0.1241073141809e+02,
5489 0.9001711808932e-08, 0.2849815827227e+01, 0.6281591679874e+01,
5490 0.8994041507257e-08, 0.3795244450750e+01, 0.6284560021018e+01,
5491 0.8298582787358e-08, 0.5236413127363e+00, 0.1241658836951e+02,
5492
5493 0.8526596520710e-08, 0.4794605424426e+01, 0.1098419223922e+02,
5494 0.8209822103197e-08, 0.1578752370328e+01, 0.1096996532989e+02,
5495 0.6357049861094e-08, 0.5708926113761e+01, 0.1596186371003e+01,
5496 0.7370473179049e-08, 0.3842402530241e+01, 0.4061219149443e+01,
5497 0.7232154664726e-08, 0.3067548981535e+01, 0.1610006857377e+03,
5498 0.6328765494903e-08, 0.1313930030069e+01, 0.1193336791622e+02,
5499 0.8030064908595e-08, 0.3488500408886e+01, 0.8460828644453e+00,
5500 0.6275464259232e-08, 0.1532061626198e+01, 0.8531963191132e+00,
5501 0.7051897446325e-08, 0.3285859929993e+01, 0.5849364236221e+01,
5502 0.6161593705428e-08, 0.1477341999464e+01, 0.5573142801433e+01,
5503
5504 0.7754683957278e-08, 0.1586118663096e+01, 0.8662240327241e+01,
5505 0.5889928990701e-08, 0.1304887868803e+01, 0.1232342296471e+02,
5506 0.5705756047075e-08, 0.4555333589350e+01, 0.1258692712880e+02,
5507 0.5964178808332e-08, 0.3001762842062e+01, 0.5333900173445e+01,
5508 0.6712446027467e-08, 0.4886780007595e+01, 0.1171295538178e+02,
5509 0.5941809275464e-08, 0.4701509603824e+01, 0.9779108567966e+01,
5510 0.5466993627395e-08, 0.4588357817278e+01, 0.1884211409667e+02,
5511 0.6340512090980e-08, 0.1164543038893e+01, 0.5217580628120e+02,
5512 0.6325505710045e-08, 0.3919171259645e+01, 0.1041998632314e+02,
5513 0.6164789509685e-08, 0.2143828253542e+01, 0.6151533897323e+01,
5514
5515 0.5263330812430e-08, 0.6066564434241e+01, 0.1885275071096e+02,
5516 0.5597087780221e-08, 0.2926316429472e+01, 0.4337116142245e+00,
5517 0.5396556236817e-08, 0.3244303591505e+01, 0.6286362197481e+01,
5518 0.5396615148223e-08, 0.3404304703662e+01, 0.6279789503410e+01,
5519 0.7091832443341e-08, 0.8532377803192e+00, 0.4907302013889e+01,
5520 0.6572352589782e-08, 0.4901966774419e+01, 0.1176433076753e+02,
5521 0.5960236060795e-08, 0.1874672315797e+01, 0.1422690933580e-01,
5522 0.5125480043511e-08, 0.3735726064334e+01, 0.1245594543367e+02,
5523 0.5928241866410e-08, 0.4502033899935e+01, 0.6414617803568e+01,
5524 0.5249600357424e-08, 0.4372334799878e+01, 0.1151388321134e+02,
5525
5526 0.6059171276087e-08, 0.2581617302908e+01, 0.6062663316000e+01,
5527 0.5295235081662e-08, 0.2974811513158e+01, 0.3496032717521e+01,
5528 0.5820561875933e-08, 0.1796073748244e+00, 0.2838593341516e+00,
5529 0.4754696606440e-08, 0.1981998136973e+01, 0.3104930017775e+01,
5530 0.6385053548955e-08, 0.2559174171605e+00, 0.6133512519065e+01,
5531 0.6589828273941e-08, 0.2750967106776e+01, 0.4087944051283e+02,
5532 0.5383376567189e-08, 0.6325947523578e+00, 0.2248384854122e+02,
5533 0.5928941683538e-08, 0.1672304519067e+01, 0.1581959461667e+01,
5534 0.4816060709794e-08, 0.3512566172575e+01, 0.9388005868221e+01,
5535 0.6003381586512e-08, 0.5610932219189e+01, 0.5326786718777e+01,
5536
5537 0.5504225393105e-08, 0.4037501131256e+01, 0.6503488384892e+01,
5538 0.5353772620129e-08, 0.6122774968240e+01, 0.1735668374386e+03,
5539 0.5786253768544e-08, 0.5527984999515e+01, 0.1350651127443e+00,
5540 0.5065706702002e-08, 0.9980765573624e+00, 0.1248988586463e+02,
5541 0.5972838885276e-08, 0.6044489493203e+01, 0.2673594526851e+02,
5542 0.5323585877961e-08, 0.3924265998147e+01, 0.4171425416666e+01,
5543 0.5210772682858e-08, 0.6220111376901e+01, 0.2460261242967e+02,
5544 0.4726549040535e-08, 0.3716043206862e+01, 0.7232251527446e+01,
5545 0.6029425105059e-08, 0.8548704071116e+00, 0.3227113045244e+03,
5546 0.4481542826513e-08, 0.1426925072829e+01, 0.5547199253223e+01,
5547
5548 0.5836024505068e-08, 0.7135651752625e-01, 0.7285056171570e+02,
5549 0.4137046613272e-08, 0.5330767643283e+01, 0.1087398597200e+02,
5550 0.5171977473924e-08, 0.4494262335353e+00, 0.1884570439172e+02,
5551 0.5694429833732e-08, 0.2952369582215e+01, 0.9723862754494e+02,
5552 0.4009158925298e-08, 0.3500003416535e+01, 0.6244942932314e+01,
5553 0.4784939596873e-08, 0.6196709413181e+01, 0.2929661536378e+02,
5554 0.3983725022610e-08, 0.5103690031897e+01, 0.4274518229222e+01,
5555 0.3870535232462e-08, 0.3187569587401e+01, 0.6321208768577e+01,
5556 0.5140501213951e-08, 0.1668924357457e+01, 0.1232032006293e+02,
5557 0.3849034819355e-08, 0.4445722510309e+01, 0.1726726808967e+02,
5558
5559 0.4002383075060e-08, 0.5226224152423e+01, 0.7018952447668e+01,
5560 0.3890719543549e-08, 0.4371166550274e+01, 0.1491901785440e+02,
5561 0.4887084607881e-08, 0.5973556689693e+01, 0.1478866649112e+01,
5562 0.3739939287592e-08, 0.2089084714600e+01, 0.6922973089781e+01,
5563 0.5031925918209e-08, 0.4658371936827e+01, 0.1715706182245e+02,
5564 0.4387748764954e-08, 0.4825580552819e+01, 0.2331413144044e+03,
5565 0.4147398098865e-08, 0.3739003524998e+01, 0.1376059875786e+02,
5566 0.3719089993586e-08, 0.1148941386536e+01, 0.6297302759782e+01,
5567 0.3934238461056e-08, 0.1559893008343e+01, 0.7872148766781e+01,
5568 0.3672471375622e-08, 0.5516145383612e+01, 0.6268848941110e+01,
5569
5570 0.3768911277583e-08, 0.6116053700563e+01, 0.4157198507331e+01,
5571 0.4033388417295e-08, 0.5076821746017e+01, 0.1567108171867e+02,
5572 0.3764194617832e-08, 0.8164676232075e+00, 0.3185192151914e+01,
5573 0.4840628226284e-08, 0.1360479453671e+01, 0.1252801878276e+02,
5574 0.4949443923785e-08, 0.2725622229926e+01, 0.1617106187867e+03,
5575 0.4117393089971e-08, 0.6054459628492e+00, 0.5642198095270e+01,
5576 0.3925754020428e-08, 0.8570462135210e+00, 0.2139354194808e+02,
5577 0.3630551757923e-08, 0.3552067338279e+01, 0.6294805223347e+01,
5578 0.3627274802357e-08, 0.3096565085313e+01, 0.6271346477544e+01,
5579 0.3806143885093e-08, 0.6367751709777e+00, 0.1725304118033e+02,
5580
5581 0.4433254641565e-08, 0.4848461503937e+01, 0.7445550607224e+01,
5582 0.3712319846576e-08, 0.1331950643655e+01, 0.4194847048887e+00,
5583 0.3849847534783e-08, 0.4958368297746e+00, 0.9562891316684e+00,
5584 0.3483955430165e-08, 0.2237215515707e+01, 0.1161697602389e+02,
5585 0.3961912730982e-08, 0.3332402188575e+01, 0.2277943724828e+02,
5586 0.3419978244481e-08, 0.5785600576016e+01, 0.1362553364512e+02,
5587 0.3329417758177e-08, 0.9812676559709e-01, 0.1685848245639e+02,
5588 0.4207206893193e-08, 0.9494780468236e+00, 0.2986433403208e+02,
5589 0.3268548976410e-08, 0.1739332095686e+00, 0.5749861718712e+01,
5590 0.3321880082685e-08, 0.1423354800666e+01, 0.6279143387820e+01,
5591
5592 0.4503173010852e-08, 0.2314972675293e+00, 0.1385561574497e+01,
5593 0.4316599090954e-08, 0.1012646782616e+00, 0.4176041334900e+01,
5594 0.3283493323850e-08, 0.5233306881265e+01, 0.6287008313071e+01,
5595 0.3164033542343e-08, 0.4005597257511e+01, 0.2099539292909e+02,
5596 0.4159720956725e-08, 0.5365676242020e+01, 0.5905702259363e+01,
5597 0.3565176892217e-08, 0.4284440620612e+01, 0.3932462625300e-02,
5598 0.3514440950221e-08, 0.4270562636575e+01, 0.7335344340001e+01,
5599 0.3540596871909e-08, 0.5953553201060e+01, 0.1234573916645e+02,
5600 0.2960769905118e-08, 0.1115180417718e+01, 0.2670964694522e+02,
5601 0.2962213739684e-08, 0.3863811918186e+01, 0.6408777551755e+00,
5602
5603 0.3883556700251e-08, 0.1268617928302e+01, 0.6660449441528e+01,
5604 0.2919225516346e-08, 0.4908605223265e+01, 0.1375773836557e+01,
5605 0.3115158863370e-08, 0.3744519976885e+01, 0.3802769619140e-01,
5606 0.4099438144212e-08, 0.4173244670532e+01, 0.4480965020977e+02,
5607 0.2899531858964e-08, 0.5910601428850e+01, 0.2059724391010e+02,
5608 0.3289733429855e-08, 0.2488050078239e+01, 0.1081813534213e+02,
5609 0.3933075612875e-08, 0.1122363652883e+01, 0.3773735910827e+00,
5610 0.3021403764467e-08, 0.4951973724904e+01, 0.2982630633589e+02,
5611 0.2798598949757e-08, 0.5117057845513e+01, 0.1937891852345e+02,
5612 0.3397421302707e-08, 0.6104159180476e+01, 0.6923953605621e+01,
5613
5614 0.3720398002179e-08, 0.1184933429829e+01, 0.3066615496545e+02,
5615 0.3598484186267e-08, 0.3505282086105e+01, 0.6147450479709e+01,
5616 0.3694594027310e-08, 0.2286651088141e+01, 0.2636725487657e+01,
5617 0.2680444152969e-08, 0.1871816775482e+00, 0.6816289982179e+01,
5618 0.3497574865641e-08, 0.3143251755431e+01, 0.6418701221183e+01,
5619 0.3130274129494e-08, 0.2462167316018e+01, 0.1235996607578e+02,
5620 0.3241119069551e-08, 0.4256374004686e+01, 0.1652265972112e+02,
5621 0.2601960842061e-08, 0.4970362941425e+01, 0.1045450126711e+02,
5622 0.2690601527504e-08, 0.2372657824898e+01, 0.3163918923335e+00,
5623 0.2908688152664e-08, 0.4232652627721e+01, 0.2828699048865e+02,
5624
5625 0.3120456131875e-08, 0.3925747001137e+00, 0.2195415756911e+02,
5626 0.3148855423384e-08, 0.3093478330445e+01, 0.1172006883645e+02,
5627 0.3051044261017e-08, 0.5560948248212e+01, 0.6055599646783e+01,
5628 0.2826006876660e-08, 0.5072790310072e+01, 0.5120601093667e+01,
5629 0.3100034191711e-08, 0.4998530231096e+01, 0.1799603123222e+02,
5630 0.2398771640101e-08, 0.2561739802176e+01, 0.6255674361143e+01,
5631 0.2384002842728e-08, 0.4087420284111e+01, 0.6310477339748e+01,
5632 0.2842146517568e-08, 0.2515048217955e+01, 0.5469525544182e+01,
5633 0.2847674371340e-08, 0.5235326497443e+01, 0.1034429499989e+02,
5634 0.2903722140764e-08, 0.1088200795797e+01, 0.6510552054109e+01,
5635
5636 0.3187610710605e-08, 0.4710624424816e+01, 0.1693792562116e+03,
5637 0.3048869992813e-08, 0.2857975896445e+00, 0.8390110365991e+01,
5638 0.2860216950984e-08, 0.2241619020815e+01, 0.2243449970715e+00,
5639 0.2701117683113e-08, 0.6651573305272e-01, 0.6129297044991e+01,
5640 0.2509891590152e-08, 0.1285135324585e+01, 0.1044027435778e+02,
5641 0.2623200252223e-08, 0.2981229834530e+00, 0.6436854655901e+01,
5642 0.2622541669202e-08, 0.6122470726189e+01, 0.9380959548977e+01,
5643 0.2818435667099e-08, 0.4251087148947e+01, 0.5934151399930e+01,
5644 0.2365196797465e-08, 0.3465070460790e+01, 0.2470570524223e+02,
5645 0.2358704646143e-08, 0.5791603815350e+01, 0.8671969964381e+01,
5646
5647 0.2388299481390e-08, 0.4142483772941e+01, 0.7096626156709e+01,
5648 0.1996041217224e-08, 0.2101901889496e+01, 0.1727188400790e+02,
5649 0.2687593060336e-08, 0.1526689456959e+01, 0.7075506709219e+02,
5650 0.2618913670810e-08, 0.2397684236095e+01, 0.6632000300961e+01,
5651 0.2571523050364e-08, 0.5751929456787e+00, 0.6206810014183e+01,
5652 0.2582135006946e-08, 0.5595464352926e+01, 0.4873985990671e+02,
5653 0.2372530190361e-08, 0.5092689490655e+01, 0.1590676413561e+02,
5654 0.2357178484712e-08, 0.4444363527851e+01, 0.3097883698531e+01,
5655 0.2451590394723e-08, 0.3108251687661e+01, 0.6612329252343e+00,
5656 0.2370045949608e-08, 0.2608133861079e+01, 0.3459636466239e+02,
5657
5658 0.2268997267358e-08, 0.3639717753384e+01, 0.2844914056730e-01,
5659 0.1731432137906e-08, 0.1741898445707e+00, 0.2019909489111e+02,
5660 0.1629869741622e-08, 0.3902225646724e+01, 0.3035599730800e+02,
5661 0.2206215801974e-08, 0.4971131250731e+01, 0.6281667977667e+01,
5662 0.2205469554680e-08, 0.1677462357110e+01, 0.6284483723224e+01,
5663 0.2148792362509e-08, 0.4236259604006e+01, 0.1980482729015e+02,
5664 0.1873733657847e-08, 0.5926814998687e+01, 0.2876692439167e+02,
5665 0.2026573758959e-08, 0.4349643351962e+01, 0.2449240616245e+02,
5666 0.1807770325110e-08, 0.5700940482701e+01, 0.2045286941806e+02,
5667 0.1881174408581e-08, 0.6601286363430e+00, 0.2358125818164e+02,
5668
5669 0.1368023671690e-08, 0.2211098592752e+01, 0.2473415438279e+02,
5670 0.1720017916280e-08, 0.4942488551129e+01, 0.1679593901136e+03,
5671 0.1702427665131e-08, 0.1452233856386e+01, 0.3338575901272e+03,
5672 0.1414032510054e-08, 0.5525357721439e+01, 0.1624205518357e+03,
5673 0.1652626045364e-08, 0.4108794283624e+01, 0.8956999012000e+02,
5674 0.1642957769686e-08, 0.7344335209984e+00, 0.5267006960365e+02,
5675 0.1614952403624e-08, 0.3541213951363e+01, 0.3332657872986e+02,
5676 0.1535988291188e-08, 0.4031094072151e+01, 0.3852657435933e+02,
5677 0.1593193738177e-08, 0.4185136203609e+01, 0.2282781046519e+03,
5678 0.1074569126382e-08, 0.1720485636868e+01, 0.8397383534231e+02,
5679
5680 0.1074408214509e-08, 0.2758613420318e+01, 0.8401985929482e+02,
5681 0.9700199670465e-09, 0.4216686842097e+01, 0.7826370942180e+02,
5682 0.1258433517061e-08, 0.2575068876639e+00, 0.3115650189215e+03,
5683 0.1240303229539e-08, 0.4800844956756e+00, 0.1784300471910e+03,
5684 0.9018345948127e-09, 0.3896756361552e+00, 0.5886454391678e+02,
5685 0.1135301432805e-08, 0.3700805023550e+00, 0.7842370451713e+02,
5686 0.9215887951370e-09, 0.4364579276638e+01, 0.1014262087719e+03,
5687 0.1055401054147e-08, 0.2156564222111e+01, 0.5660027930059e+02,
5688 0.1008725979831e-08, 0.5454015785234e+01, 0.4245678405627e+02,
5689 0.7217398104321e-09, 0.1597772562175e+01, 0.2457074661053e+03,
5690
5691 0.6912033134447e-09, 0.5824090621461e+01, 0.1679936946371e+03,
5692 0.6833881523549e-09, 0.3578778482835e+01, 0.6053048899753e+02,
5693 0.4887304205142e-09, 0.3724362812423e+01, 0.9656299901946e+02,
5694 0.5173709754788e-09, 0.5422427507933e+01, 0.2442876000072e+03,
5695 0.4671353097145e-09, 0.2396106924439e+01, 0.1435713242844e+03,
5696 0.5652608439480e-09, 0.2804028838685e+01, 0.8365903305582e+02,
5697 0.5604061331253e-09, 0.1638816006247e+01, 0.8433466158131e+02,
5698 0.4712723365400e-09, 0.8979003224474e+00, 0.3164282286739e+03,
5699 0.4909967465112e-09, 0.3210426725516e+01, 0.4059982187939e+03,
5700 0.4771358267658e-09, 0.5308027211629e+01, 0.1805255418145e+03,
5701
5702 0.3943451445989e-09, 0.2195145341074e+01, 0.2568537517081e+03,
5703 0.3952109120244e-09, 0.5081189491586e+01, 0.2449975330562e+03,
5704 0.3788134594789e-09, 0.4345171264441e+01, 0.1568131045107e+03,
5705 0.3738330190479e-09, 0.2613062847997e+01, 0.3948519331910e+03,
5706 0.3099866678136e-09, 0.2846760817689e+01, 0.1547176098872e+03,
5707 0.2002962716768e-09, 0.4921360989412e+01, 0.2268582385539e+03,
5708 0.2198291338754e-09, 0.1130360117454e+00, 0.1658638954901e+03,
5709 0.1491958330784e-09, 0.4228195232278e+01, 0.2219950288015e+03,
5710 0.1475384076173e-09, 0.3005721811604e+00, 0.3052819430710e+03,
5711 0.1661626624624e-09, 0.7830125621203e+00, 0.2526661704812e+03,
5712
5713 0.9015823460025e-10, 0.3807792942715e+01, 0.4171445043968e+03 };
5714
5715 /* Sun-to-Earth, T^0, Y */
5716 static final double e0y[] = {
5717 0.9998921098898e+00, 0.1826583913846e+00, 0.6283075850446e+01,
5718 -0.2442700893735e-01, 0.0000000000000e+00, 0.0000000000000e+00,
5719 0.8352929742915e-02, 0.1395277998680e+00, 0.1256615170089e+02,
5720 0.1046697300177e-03, 0.9641423109763e-01, 0.1884922755134e+02,
5721 0.3110841876663e-04, 0.5381140401712e+01, 0.8399684731857e+02,
5722 0.2570269094593e-04, 0.5301016407128e+01, 0.5296909721118e+00,
5723 0.2147389623610e-04, 0.2662510869850e+01, 0.1577343543434e+01,
5724 0.1680344384050e-04, 0.5207904119704e+01, 0.6279552690824e+01,
5725 0.1679117312193e-04, 0.4582187486968e+01, 0.6286599010068e+01,
5726 0.1440512068440e-04, 0.1900688517726e+01, 0.2352866153506e+01,
5727
5728 0.1135139664999e-04, 0.5273108538556e+01, 0.5223693906222e+01,
5729 0.9345482571018e-05, 0.4503047687738e+01, 0.1203646072878e+02,
5730 0.9007418719568e-05, 0.1605621059637e+01, 0.1021328554739e+02,
5731 0.5671536712314e-05, 0.5812849070861e+00, 0.1059381944224e+01,
5732 0.7451401861666e-05, 0.2807346794836e+01, 0.3981490189893e+00,
5733 0.6393470057114e-05, 0.6029224133855e+01, 0.5753384878334e+01,
5734 0.6814275881697e-05, 0.6472990145974e+00, 0.4705732307012e+01,
5735 0.6113705628887e-05, 0.3813843419700e+01, 0.6812766822558e+01,
5736 0.4503851367273e-05, 0.4527804370996e+01, 0.5884926831456e+01,
5737 0.4522249141926e-05, 0.5991783029224e+01, 0.6256777527156e+01,
5738
5739 0.4501794307018e-05, 0.3798703844397e+01, 0.6309374173736e+01,
5740 0.5514927480180e-05, 0.3961257833388e+01, 0.5507553240374e+01,
5741 0.4062862799995e-05, 0.5256247296369e+01, 0.6681224869435e+01,
5742 0.5414900429712e-05, 0.5499032014097e+01, 0.7755226100720e+00,
5743 0.5463153987424e-05, 0.6173092454097e+01, 0.1414349524433e+02,
5744 0.5071611859329e-05, 0.2870244247651e+01, 0.7860419393880e+01,
5745 0.2195112094455e-05, 0.2952338617201e+01, 0.1150676975667e+02,
5746 0.2279139233919e-05, 0.5951775132933e+01, 0.7058598460518e+01,
5747 0.2278386100876e-05, 0.4845456398785e+01, 0.4694002934110e+01,
5748 0.2559088003308e-05, 0.6945321117311e+00, 0.1216800268190e+02,
5749
5750 0.2561079286856e-05, 0.6167224608301e+01, 0.7099330490126e+00,
5751 0.1792755796387e-05, 0.1400122509632e+01, 0.7962980379786e+00,
5752 0.1818715656502e-05, 0.4703347611830e+01, 0.6283142985870e+01,
5753 0.1818744924791e-05, 0.5086748900237e+01, 0.6283008715021e+01,
5754 0.1554518791390e-05, 0.5331008042713e-01, 0.2513230340178e+02,
5755 0.2063265737239e-05, 0.4283680484178e+01, 0.1179062909082e+02,
5756 0.1497613520041e-05, 0.6074207826073e+01, 0.5486777812467e+01,
5757 0.2000617940427e-05, 0.2501426281450e+01, 0.1778984560711e+02,
5758 0.1289731195580e-05, 0.3646340599536e+01, 0.7079373888424e+01,
5759 0.1282657998934e-05, 0.3232864804902e+01, 0.3738761453707e+01,
5760
5761 0.1528915968658e-05, 0.5581433416669e+01, 0.2132990797783e+00,
5762 0.1187304098432e-05, 0.5453576453694e+01, 0.9437762937313e+01,
5763 0.7842782928118e-06, 0.2823953922273e+00, 0.8827390247185e+01,
5764 0.7352892280868e-06, 0.1124369580175e+01, 0.1589072916335e+01,
5765 0.6570189360797e-06, 0.2089154042840e+01, 0.1176985366291e+02,
5766 0.6324967590410e-06, 0.6704855581230e+00, 0.6262300422539e+01,
5767 0.6298289872283e-06, 0.2836414855840e+01, 0.6303851278352e+01,
5768 0.6476686465855e-06, 0.4852433866467e+00, 0.7113454667900e-02,
5769 0.8587034651234e-06, 0.1453511005668e+01, 0.1672837615881e+03,
5770 0.8068948788113e-06, 0.9224087798609e+00, 0.6069776770667e+01,
5771
5772 0.8353786011661e-06, 0.4631707184895e+01, 0.3340612434717e+01,
5773 0.6009324532132e-06, 0.1829498827726e+01, 0.4136910472696e+01,
5774 0.7558158559566e-06, 0.2588596800317e+01, 0.6496374930224e+01,
5775 0.5809279504503e-06, 0.5516818853476e+00, 0.1097707878456e+02,
5776 0.5374131950254e-06, 0.6275674734960e+01, 0.1194447056968e+01,
5777 0.5711160507326e-06, 0.1091905956872e+01, 0.6282095334605e+01,
5778 0.5710183170746e-06, 0.2415001635090e+01, 0.6284056366286e+01,
5779 0.5144373590610e-06, 0.6020336443438e+01, 0.6290189305114e+01,
5780 0.5103108927267e-06, 0.3775634564605e+01, 0.6275962395778e+01,
5781 0.4960654697891e-06, 0.1073450946756e+01, 0.6127655567643e+01,
5782
5783 0.4786385689280e-06, 0.2431178012310e+01, 0.6438496133249e+01,
5784 0.6109911263665e-06, 0.5343356157914e+01, 0.3154687086868e+01,
5785 0.4839898944024e-06, 0.5830833594047e-01, 0.8018209333619e+00,
5786 0.4734822623919e-06, 0.4536080134821e+01, 0.3128388763578e+01,
5787 0.4834741473290e-06, 0.2585090489754e+00, 0.7084896783808e+01,
5788 0.5134858581156e-06, 0.4213317172603e+01, 0.1235285262111e+02,
5789 0.5064004264978e-06, 0.4814418806478e+00, 0.1185621865188e+02,
5790 0.3753476772761e-06, 0.1599953399788e+01, 0.8429241228195e+01,
5791 0.4935264014283e-06, 0.2157417556873e+01, 0.2544314396739e+01,
5792 0.3950929600897e-06, 0.3359394184254e+01, 0.5481254917084e+01,
5793
5794 0.4895849789777e-06, 0.5165704376558e+01, 0.9225539266174e+01,
5795 0.4215241688886e-06, 0.2065368800993e+01, 0.1726015463500e+02,
5796 0.3796773731132e-06, 0.1468606346612e+01, 0.4265981595566e+00,
5797 0.3114178142515e-06, 0.3615638079474e+01, 0.2146165377750e+01,
5798 0.3260664220838e-06, 0.4417134922435e+01, 0.4164311961999e+01,
5799 0.3976996123008e-06, 0.4700866883004e+01, 0.5856477690889e+01,
5800 0.2801459672924e-06, 0.4538902060922e+01, 0.1256967486051e+02,
5801 0.3638931868861e-06, 0.1334197991475e+01, 0.1807370494127e+02,
5802 0.2487013269476e-06, 0.3749275558275e+01, 0.2629832328990e-01,
5803 0.3034165481994e-06, 0.4236622030873e+00, 0.4535059491685e+01,
5804
5805 0.2676278825586e-06, 0.5970848007811e+01, 0.3930209696940e+01,
5806 0.2764903818918e-06, 0.5194636754501e+01, 0.1256262854127e+02,
5807 0.2485149930507e-06, 0.1002434207846e+01, 0.5088628793478e+01,
5808 0.2199305540941e-06, 0.3066773098403e+01, 0.1255903824622e+02,
5809 0.2571106500435e-06, 0.7588312459063e+00, 0.1336797263425e+02,
5810 0.2049751817158e-06, 0.3444977434856e+01, 0.1137170464392e+02,
5811 0.2599707296297e-06, 0.1873128542205e+01, 0.7143069561767e+02,
5812 0.1785018072217e-06, 0.5015891306615e+01, 0.1748016358760e+01,
5813 0.2324833891115e-06, 0.4618271239730e+01, 0.1831953657923e+02,
5814 0.1709711119545e-06, 0.5300003455669e+01, 0.4933208510675e+01,
5815
5816 0.2107159351716e-06, 0.2229819815115e+01, 0.7477522907414e+01,
5817 0.1750333080295e-06, 0.6161485880008e+01, 0.1044738781244e+02,
5818 0.2000598210339e-06, 0.2967357299999e+01, 0.8031092209206e+01,
5819 0.1380920248681e-06, 0.3027007923917e+01, 0.8635942003952e+01,
5820 0.1412460470299e-06, 0.6037597163798e+01, 0.2942463415728e+01,
5821 0.1888459803001e-06, 0.8561476243374e+00, 0.1561374759853e+03,
5822 0.1788370542585e-06, 0.4869736290209e+01, 0.1592596075957e+01,
5823 0.1360893296167e-06, 0.3626411886436e+01, 0.1309584267300e+02,
5824 0.1506846530160e-06, 0.1550975377427e+01, 0.1649636139783e+02,
5825 0.1800913376176e-06, 0.2075826033190e+01, 0.1729818233119e+02,
5826
5827 0.1436261390649e-06, 0.6148876420255e+01, 0.2042657109477e+02,
5828 0.1220227114151e-06, 0.4382583879906e+01, 0.7632943190217e+01,
5829 0.1337883603592e-06, 0.2036644327361e+01, 0.1213955354133e+02,
5830 0.1159326650738e-06, 0.3892276994687e+01, 0.5331357529664e+01,
5831 0.1352853128569e-06, 0.1447950649744e+01, 0.1673046366289e+02,
5832 0.1433408296083e-06, 0.4457854692961e+01, 0.7342457794669e+01,
5833 0.1234701666518e-06, 0.1538818147151e+01, 0.6279485555400e+01,
5834 0.1234027192007e-06, 0.1968523220760e+01, 0.6286666145492e+01,
5835 0.1244024091797e-06, 0.5779803499985e+01, 0.1511046609763e+02,
5836 0.1097934945516e-06, 0.6210975221388e+00, 0.1098880815746e+02,
5837
5838 0.1254611329856e-06, 0.2591963807998e+01, 0.1572083878776e+02,
5839 0.1158247286784e-06, 0.2483612812670e+01, 0.5729506548653e+01,
5840 0.9039078252960e-07, 0.3857554579796e+01, 0.9623688285163e+01,
5841 0.9108024978836e-07, 0.5826368512984e+01, 0.7234794171227e+01,
5842 0.8887068108436e-07, 0.3475694573987e+01, 0.6148010737701e+01,
5843 0.8632374035438e-07, 0.3059070488983e-01, 0.6418140963190e+01,
5844 0.7893186992967e-07, 0.1583194837728e+01, 0.2118763888447e+01,
5845 0.8297650201172e-07, 0.8519770534637e+00, 0.1471231707864e+02,
5846 0.1019759578988e-06, 0.1319598738732e+00, 0.1349867339771e+01,
5847 0.1010037696236e-06, 0.9937860115618e+00, 0.6836645152238e+01,
5848
5849 0.1047727548266e-06, 0.1382138405399e+01, 0.5999216516294e+01,
5850 0.7351993881086e-07, 0.3833397851735e+01, 0.6040347114260e+01,
5851 0.9868771092341e-07, 0.2124913814390e+01, 0.6566935184597e+01,
5852 0.7007321959390e-07, 0.5946305343763e+01, 0.6525804586632e+01,
5853 0.6861411679709e-07, 0.4574654977089e+01, 0.7238675589263e+01,
5854 0.7554519809614e-07, 0.5949232686844e+01, 0.1253985337760e+02,
5855 0.9541880448335e-07, 0.3495242990564e+01, 0.2122839202813e+02,
5856 0.7185606722155e-07, 0.4310113471661e+01, 0.6245048154254e+01,
5857 0.7131360871710e-07, 0.5480309323650e+01, 0.6321103546637e+01,
5858 0.6651142021039e-07, 0.5411097713654e+01, 0.5327476111629e+01,
5859
5860 0.8538618213667e-07, 0.1827849973951e+01, 0.1101510648075e+02,
5861 0.8634954288044e-07, 0.5443584943349e+01, 0.5643178611111e+01,
5862 0.7449415051484e-07, 0.2011535459060e+01, 0.5368044267797e+00,
5863 0.7421047599169e-07, 0.3464562529249e+01, 0.2354323048545e+02,
5864 0.6140694354424e-07, 0.5657556228815e+01, 0.1296430071988e+02,
5865 0.6353525143033e-07, 0.3463816593821e+01, 0.1990745094947e+01,
5866 0.6221964013447e-07, 0.1532259498697e+01, 0.9517183207817e+00,
5867 0.5852480257244e-07, 0.1375396598875e+01, 0.9555997388169e+00,
5868 0.6398637498911e-07, 0.2405645801972e+01, 0.2407292145756e+02,
5869 0.7039744069878e-07, 0.5397541799027e+01, 0.5225775174439e+00,
5870
5871 0.6977997694382e-07, 0.4762347105419e+01, 0.1097355562493e+02,
5872 0.7460629558396e-07, 0.2711944692164e+01, 0.2200391463820e+02,
5873 0.5376577536101e-07, 0.2352980430239e+01, 0.1431416805965e+02,
5874 0.7530607893556e-07, 0.1943940180699e+01, 0.1842262939178e+02,
5875 0.6822928971605e-07, 0.4337651846959e+01, 0.1554202828031e+00,
5876 0.6220772380094e-07, 0.6716871369278e+00, 0.1845107853235e+02,
5877 0.6586950799043e-07, 0.2229714460505e+01, 0.5216580451554e+01,
5878 0.5873800565771e-07, 0.7627013920580e+00, 0.6398972393349e+00,
5879 0.6264346929745e-07, 0.6202785478961e+00, 0.6277552955062e+01,
5880 0.6257929115669e-07, 0.2886775596668e+01, 0.6288598745829e+01,
5881
5882 0.5343536033409e-07, 0.1977241012051e+01, 0.4690479774488e+01,
5883 0.5587849781714e-07, 0.1922923484825e+01, 0.1551045220144e+01,
5884 0.6905100845603e-07, 0.3570757164631e+01, 0.1030928125552e+00,
5885 0.6178957066649e-07, 0.5197558947765e+01, 0.5230807360890e+01,
5886 0.6187270224331e-07, 0.8193497368922e+00, 0.5650292065779e+01,
5887 0.5385664291426e-07, 0.5406336665586e+01, 0.7771377146812e+02,
5888 0.6329363917926e-07, 0.2837760654536e+01, 0.2608790314060e+02,
5889 0.4546018761604e-07, 0.2933580297050e+01, 0.5535693017924e+00,
5890 0.6196091049375e-07, 0.4157871494377e+01, 0.8467247584405e+02,
5891 0.6159555108218e-07, 0.3211703561703e+01, 0.2394243902548e+03,
5892
5893 0.4995340539317e-07, 0.1459098102922e+01, 0.4732030630302e+01,
5894 0.5457031243572e-07, 0.1430457676136e+01, 0.6179983037890e+01,
5895 0.4863461418397e-07, 0.2196425916730e+01, 0.9027992316901e+02,
5896 0.5342947626870e-07, 0.2086612890268e+01, 0.6386168663001e+01,
5897 0.5674296648439e-07, 0.2760204966535e+01, 0.6915859635113e+01,
5898 0.4745783120161e-07, 0.4245368971862e+01, 0.6282970628506e+01,
5899 0.4745676961198e-07, 0.5544725787016e+01, 0.6283181072386e+01,
5900 0.4049796869973e-07, 0.2213984363586e+01, 0.6254626709878e+01,
5901 0.4248333596940e-07, 0.8075781952896e+00, 0.7875671926403e+01,
5902 0.4027178070205e-07, 0.1293268540378e+01, 0.6311524991013e+01,
5903
5904 0.4066543943476e-07, 0.3986141175804e+01, 0.3634620989887e+01,
5905 0.4858863787880e-07, 0.1276112738231e+01, 0.5760498333002e+01,
5906 0.5277398263530e-07, 0.4916111741527e+01, 0.2515860172507e+02,
5907 0.4105635656559e-07, 0.1725805864426e+01, 0.6709674010002e+01,
5908 0.4376781925772e-07, 0.2243642442106e+01, 0.6805653367890e+01,
5909 0.3235827894693e-07, 0.3614135118271e+01, 0.1066495398892e+01,
5910 0.3073244740308e-07, 0.2460873393460e+01, 0.5863591145557e+01,
5911 0.3088609271373e-07, 0.5678431771790e+01, 0.9917696840332e+01,
5912 0.3393022279836e-07, 0.3814017477291e+01, 0.1391601904066e+02,
5913 0.3038686508802e-07, 0.4660216229171e+01, 0.1256621883632e+02,
5914
5915 0.4019677752497e-07, 0.5906906243735e+01, 0.1334167431096e+02,
5916 0.3288834998232e-07, 0.9536146445882e+00, 0.1620077269078e+02,
5917 0.3889973794631e-07, 0.3942205097644e+01, 0.7478166569050e-01,
5918 0.3050438987141e-07, 0.1624810271286e+01, 0.1805292951336e+02,
5919 0.3601142564638e-07, 0.4030467142575e+01, 0.6208294184755e+01,
5920 0.3689015557141e-07, 0.3648878818694e+01, 0.5966683958112e+01,
5921 0.3563471893565e-07, 0.5749584017096e+01, 0.6357857516136e+01,
5922 0.2776183170667e-07, 0.2630124187070e+01, 0.3523159621801e-02,
5923 0.2922350530341e-07, 0.1790346403629e+01, 0.1272157198369e+02,
5924 0.3511076917302e-07, 0.6142198301611e+01, 0.6599467742779e+01,
5925
5926 0.3619351007632e-07, 0.1432421386492e+01, 0.6019991944201e+01,
5927 0.2561254711098e-07, 0.2302822475792e+01, 0.1259245002418e+02,
5928 0.2626903942920e-07, 0.8660470994571e+00, 0.6702560555334e+01,
5929 0.2550187397083e-07, 0.6069721995383e+01, 0.1057540660594e+02,
5930 0.2535873526138e-07, 0.1079020331795e-01, 0.3141537925223e+02,
5931 0.3519786153847e-07, 0.3809066902283e+01, 0.2505706758577e+03,
5932 0.3424651492873e-07, 0.2075435114417e+01, 0.6546159756691e+01,
5933 0.2372676630861e-07, 0.2057803120154e+01, 0.2388894113936e+01,
5934 0.2710980779541e-07, 0.1510068488010e+01, 0.1202934727411e+02,
5935 0.3038710889704e-07, 0.5043617528901e+01, 0.1256608456547e+02,
5936
5937 0.2220364130585e-07, 0.3694793218205e+01, 0.1336244973887e+02,
5938 0.3025880825460e-07, 0.5450618999049e-01, 0.2908881142201e+02,
5939 0.2784493486864e-07, 0.3381164084502e+01, 0.1494531617769e+02,
5940 0.2294414142438e-07, 0.4382309025210e+01, 0.6076890225335e+01,
5941 0.2012723294724e-07, 0.9142212256518e+00, 0.6262720680387e+01,
5942 0.2036357831958e-07, 0.5676172293154e+01, 0.4701116388778e+01,
5943 0.2003474823288e-07, 0.2592767977625e+01, 0.6303431020504e+01,
5944 0.2207144900109e-07, 0.5404976271180e+01, 0.6489261475556e+01,
5945 0.2481664905135e-07, 0.4373284587027e+01, 0.1204357418345e+02,
5946 0.2674949182295e-07, 0.5859182188482e+01, 0.4590910121555e+01,
5947
5948 0.2450554720322e-07, 0.4555381557451e+01, 0.1495633313810e+00,
5949 0.2601975986457e-07, 0.3933165584959e+01, 0.1965104848470e+02,
5950 0.2199860022848e-07, 0.5227977189087e+01, 0.1351787002167e+02,
5951 0.2448121172316e-07, 0.4858060353949e+01, 0.1162474756779e+01,
5952 0.1876014864049e-07, 0.5690546553605e+01, 0.6279194432410e+01,
5953 0.1874513219396e-07, 0.4099539297446e+01, 0.6286957268481e+01,
5954 0.2156380842559e-07, 0.4382594769913e+00, 0.1813929450232e+02,
5955 0.1981691240061e-07, 0.1829784152444e+01, 0.4686889479442e+01,
5956 0.2329992648539e-07, 0.2836254278973e+01, 0.1002183730415e+02,
5957 0.1765184135302e-07, 0.2803494925833e+01, 0.4292330755499e+01,
5958
5959 0.2436368366085e-07, 0.2836897959677e+01, 0.9514313292143e+02,
5960 0.2164089203889e-07, 0.6127522446024e+01, 0.6037244212485e+01,
5961 0.1847755034221e-07, 0.3683163635008e+01, 0.2427287361862e+00,
5962 0.1674798769966e-07, 0.3316993867246e+00, 0.1311972100268e+02,
5963 0.2222542124356e-07, 0.8294097805480e+00, 0.1266924451345e+02,
5964 0.2071074505925e-07, 0.3659492220261e+01, 0.6528907488406e+01,
5965 0.1608224471835e-07, 0.4774492067182e+01, 0.1352175143971e+02,
5966 0.1857583439071e-07, 0.2873120597682e+01, 0.8662240327241e+01,
5967 0.1793018836159e-07, 0.5282441177929e+00, 0.6819880277225e+01,
5968 0.1575391221692e-07, 0.1320789654258e+01, 0.1102062672231e+00,
5969
5970 0.1840132009557e-07, 0.1917110916256e+01, 0.6514761976723e+02,
5971 0.1760917288281e-07, 0.2972635937132e+01, 0.5746271423666e+01,
5972 0.1561779518516e-07, 0.4372569261981e+01, 0.6272439236156e+01,
5973 0.1558687885205e-07, 0.5416424926425e+01, 0.6293712464735e+01,
5974 0.1951359382579e-07, 0.3094448898752e+01, 0.2301353951334e+02,
5975 0.1569144275614e-07, 0.2802103689808e+01, 0.1765478049437e+02,
5976 0.1479130389462e-07, 0.2136435020467e+01, 0.2077542790660e-01,
5977 0.1467828510764e-07, 0.7072627435674e+00, 0.1052268489556e+01,
5978 0.1627627337440e-07, 0.3947607143237e+01, 0.6327837846670e+00,
5979 0.1503498479758e-07, 0.4079248909190e+01, 0.7626583626240e-01,
5980
5981 0.1297967708237e-07, 0.6269637122840e+01, 0.1149965630200e+02,
5982 0.1374416896634e-07, 0.4175657970702e+01, 0.6016468784579e+01,
5983 0.1783812325219e-07, 0.1476540547560e+01, 0.3301902111895e+02,
5984 0.1525884228756e-07, 0.4653477715241e+01, 0.9411464614024e+01,
5985 0.1451067396763e-07, 0.2573001128225e+01, 0.1277945078067e+02,
5986 0.1297713111950e-07, 0.5612799618771e+01, 0.6549682916313e+01,
5987 0.1462784012820e-07, 0.4189661623870e+01, 0.1863592847156e+02,
5988 0.1384185980007e-07, 0.2656915472196e+01, 0.2379164476796e+01,
5989 0.1221497599801e-07, 0.5612515760138e+01, 0.1257326515556e+02,
5990 0.1560574525896e-07, 0.4783414317919e+01, 0.1887552587463e+02,
5991
5992 0.1544598372036e-07, 0.2694431138063e+01, 0.1820933031200e+02,
5993 0.1531678928696e-07, 0.4105103489666e+01, 0.2593412433514e+02,
5994 0.1349321503795e-07, 0.3082437194015e+00, 0.5120601093667e+01,
5995 0.1252030290917e-07, 0.6124072334087e+01, 0.6993008899458e+01,
5996 0.1459243816687e-07, 0.3733103981697e+01, 0.3813291813120e-01,
5997 0.1226103625262e-07, 0.1267127706817e+01, 0.2435678079171e+02,
5998 0.1019449641504e-07, 0.4367790112269e+01, 0.1725663147538e+02,
5999 0.1380789433607e-07, 0.3387201768700e+01, 0.2458316379602e+00,
6000 0.1019453421658e-07, 0.9204143073737e+00, 0.6112403035119e+01,
6001 0.1297929434405e-07, 0.5786874896426e+01, 0.1249137003520e+02,
6002
6003 0.9912677786097e-08, 0.3164232870746e+01, 0.6247047890016e+01,
6004 0.9829386098599e-08, 0.2586762413351e+01, 0.6453748665772e+01,
6005 0.1226807746104e-07, 0.6239068436607e+01, 0.5429879531333e+01,
6006 0.1192691755997e-07, 0.1867380051424e+01, 0.6290122169689e+01,
6007 0.9836499227081e-08, 0.3424716293727e+00, 0.6319103810876e+01,
6008 0.9642862564285e-08, 0.5661372990657e+01, 0.8273820945392e+01,
6009 0.1165184404862e-07, 0.5768367239093e+01, 0.1778273215245e+02,
6010 0.1175794418818e-07, 0.1657351222943e+01, 0.6276029531202e+01,
6011 0.1018948635601e-07, 0.6458292350865e+00, 0.1254537627298e+02,
6012 0.9500383606676e-08, 0.1054306140741e+01, 0.1256517118505e+02,
6013
6014 0.1227512202906e-07, 0.2505278379114e+01, 0.2248384854122e+02,
6015 0.9664792009993e-08, 0.4289737277000e+01, 0.6259197520765e+01,
6016 0.9613285666331e-08, 0.5500597673141e+01, 0.6306954180126e+01,
6017 0.1117906736211e-07, 0.2361405953468e+01, 0.1779695906178e+02,
6018 0.9611378640782e-08, 0.2851310576269e+01, 0.2061856251104e+00,
6019 0.8845354852370e-08, 0.6208777705343e+01, 0.1692165728891e+01,
6020 0.1054046966600e-07, 0.5413091423934e+01, 0.2204125344462e+00,
6021 0.1215539124483e-07, 0.5613969479755e+01, 0.8257698122054e+02,
6022 0.9932460955209e-08, 0.1106124877015e+01, 0.1017725758696e+02,
6023 0.8785804715043e-08, 0.2869224476477e+01, 0.9491756770005e+00,
6024
6025 0.8538084097562e-08, 0.6159640899344e+01, 0.6393282117669e+01,
6026 0.8648994369529e-08, 0.1374901198784e+01, 0.4804209201333e+01,
6027 0.1039063219067e-07, 0.5171080641327e+01, 0.1550861511662e+02,
6028 0.8867983926439e-08, 0.8317320304902e+00, 0.3903911373650e+01,
6029 0.8327495955244e-08, 0.3605591969180e+01, 0.6172869583223e+01,
6030 0.9243088356133e-08, 0.6114299196843e+01, 0.6267823317922e+01,
6031 0.9205657357835e-08, 0.3675153683737e+01, 0.6298328382969e+01,
6032 0.1033269714606e-07, 0.3313328813024e+01, 0.5573142801433e+01,
6033 0.8001706275552e-08, 0.2019980960053e+01, 0.2648454860559e+01,
6034 0.9171858254191e-08, 0.8992015524177e+00, 0.1498544001348e+03,
6035
6036 0.1075327150242e-07, 0.2898669963648e+01, 0.3694923081589e+02,
6037 0.9884866689828e-08, 0.4946715904478e+01, 0.1140367694411e+02,
6038 0.9541835576677e-08, 0.2371787888469e+01, 0.1256713221673e+02,
6039 0.7739903376237e-08, 0.2213775190612e+01, 0.7834121070590e+01,
6040 0.7311962684106e-08, 0.3429378787739e+01, 0.1192625446156e+02,
6041 0.9724904869624e-08, 0.6195878564404e+01, 0.2280573557157e+02,
6042 0.9251628983612e-08, 0.6511509527390e+00, 0.2787043132925e+01,
6043 0.7320763787842e-08, 0.6001083639421e+01, 0.6282655592598e+01,
6044 0.7320296650962e-08, 0.3789073265087e+01, 0.6283496108294e+01,
6045 0.7947032271039e-08, 0.1059659582204e+01, 0.1241073141809e+02,
6046
6047 0.9005277053115e-08, 0.1280315624361e+01, 0.6281591679874e+01,
6048 0.8995601652048e-08, 0.2224439106766e+01, 0.6284560021018e+01,
6049 0.8288040568796e-08, 0.5234914433867e+01, 0.1241658836951e+02,
6050 0.6359381347255e-08, 0.4137989441490e+01, 0.1596186371003e+01,
6051 0.8699572228626e-08, 0.1758411009497e+01, 0.6133512519065e+01,
6052 0.6456797542736e-08, 0.5919285089994e+01, 0.1685848245639e+02,
6053 0.7424573475452e-08, 0.5414616938827e+01, 0.4061219149443e+01,
6054 0.7235671196168e-08, 0.1496516557134e+01, 0.1610006857377e+03,
6055 0.8104015182733e-08, 0.1919918242764e+01, 0.8460828644453e+00,
6056 0.8098576535937e-08, 0.3819615855458e+01, 0.3894181736510e+01,
6057
6058 0.6275292346625e-08, 0.6244264115141e+01, 0.8531963191132e+00,
6059 0.6052432989112e-08, 0.5037731872610e+00, 0.1567108171867e+02,
6060 0.5705651535817e-08, 0.2984557271995e+01, 0.1258692712880e+02,
6061 0.5789650115138e-08, 0.6087038140697e+01, 0.1193336791622e+02,
6062 0.5512132153377e-08, 0.5855668994076e+01, 0.1232342296471e+02,
6063 0.7388890819102e-08, 0.2443128574740e+01, 0.4907302013889e+01,
6064 0.5467593991798e-08, 0.3017561234194e+01, 0.1884211409667e+02,
6065 0.6388519802999e-08, 0.5887386712935e+01, 0.5217580628120e+02,
6066 0.6106777149944e-08, 0.3483461059895e+00, 0.1422690933580e-01,
6067 0.7383420275489e-08, 0.5417387056707e+01, 0.2358125818164e+02,
6068
6069 0.5505208141738e-08, 0.2848193644783e+01, 0.1151388321134e+02,
6070 0.6310757462877e-08, 0.2349882520828e+01, 0.1041998632314e+02,
6071 0.6166904929691e-08, 0.5728575944077e+00, 0.6151533897323e+01,
6072 0.5263442042754e-08, 0.4495796125937e+01, 0.1885275071096e+02,
6073 0.5591828082629e-08, 0.1355441967677e+01, 0.4337116142245e+00,
6074 0.5397051680497e-08, 0.1673422864307e+01, 0.6286362197481e+01,
6075 0.5396992745159e-08, 0.1833502206373e+01, 0.6279789503410e+01,
6076 0.6572913000726e-08, 0.3331122065824e+01, 0.1176433076753e+02,
6077 0.5123421866413e-08, 0.2165327142679e+01, 0.1245594543367e+02,
6078 0.5930495725999e-08, 0.2931146089284e+01, 0.6414617803568e+01,
6079
6080 0.6431797403933e-08, 0.4134407994088e+01, 0.1350651127443e+00,
6081 0.5003182207604e-08, 0.3805420303749e+01, 0.1096996532989e+02,
6082 0.5587731032504e-08, 0.1082469260599e+01, 0.6062663316000e+01,
6083 0.5935263407816e-08, 0.8384333678401e+00, 0.5326786718777e+01,
6084 0.4756019827760e-08, 0.3552588749309e+01, 0.3104930017775e+01,
6085 0.6599951172637e-08, 0.4320826409528e+01, 0.4087944051283e+02,
6086 0.5902606868464e-08, 0.4811879454445e+01, 0.5849364236221e+01,
6087 0.5921147809031e-08, 0.9942628922396e-01, 0.1581959461667e+01,
6088 0.5505382581266e-08, 0.2466557607764e+01, 0.6503488384892e+01,
6089 0.5353771071862e-08, 0.4551978748683e+01, 0.1735668374386e+03,
6090
6091 0.5063282210946e-08, 0.5710812312425e+01, 0.1248988586463e+02,
6092 0.5926120403383e-08, 0.1333998428358e+01, 0.2673594526851e+02,
6093 0.5211016176149e-08, 0.4649315360760e+01, 0.2460261242967e+02,
6094 0.5347075084894e-08, 0.5512754081205e+01, 0.4171425416666e+01,
6095 0.4872609773574e-08, 0.1308025299938e+01, 0.5333900173445e+01,
6096 0.4727711321420e-08, 0.2144908368062e+01, 0.7232251527446e+01,
6097 0.6029426018652e-08, 0.5567259412084e+01, 0.3227113045244e+03,
6098 0.4321485284369e-08, 0.5230667156451e+01, 0.9388005868221e+01,
6099 0.4476406760553e-08, 0.6134081115303e+01, 0.5547199253223e+01,
6100 0.5835268277420e-08, 0.4783808492071e+01, 0.7285056171570e+02,
6101
6102 0.5172183602748e-08, 0.5161817911099e+01, 0.1884570439172e+02,
6103 0.5693571465184e-08, 0.1381646203111e+01, 0.9723862754494e+02,
6104 0.4060634965349e-08, 0.3876705259495e+00, 0.4274518229222e+01,
6105 0.3967398770473e-08, 0.5029491776223e+01, 0.3496032717521e+01,
6106 0.3943754005255e-08, 0.1923162955490e+01, 0.6244942932314e+01,
6107 0.4781323427824e-08, 0.4633332586423e+01, 0.2929661536378e+02,
6108 0.3871483781204e-08, 0.1616650009743e+01, 0.6321208768577e+01,
6109 0.5141741733997e-08, 0.9817316704659e-01, 0.1232032006293e+02,
6110 0.4002385978497e-08, 0.3656161212139e+01, 0.7018952447668e+01,
6111 0.4901092604097e-08, 0.4404098713092e+01, 0.1478866649112e+01,
6112
6113 0.3740932630345e-08, 0.5181188732639e+00, 0.6922973089781e+01,
6114 0.4387283718538e-08, 0.3254859566869e+01, 0.2331413144044e+03,
6115 0.5019197802033e-08, 0.3086773224677e+01, 0.1715706182245e+02,
6116 0.3834931695175e-08, 0.2797882673542e+01, 0.1491901785440e+02,
6117 0.3760413942497e-08, 0.2892676280217e+01, 0.1726726808967e+02,
6118 0.3719717204628e-08, 0.5861046025739e+01, 0.6297302759782e+01,
6119 0.4145623530149e-08, 0.2168239627033e+01, 0.1376059875786e+02,
6120 0.3932788425380e-08, 0.6271811124181e+01, 0.7872148766781e+01,
6121 0.3686377476857e-08, 0.3936853151404e+01, 0.6268848941110e+01,
6122 0.3779077950339e-08, 0.1404148734043e+01, 0.4157198507331e+01,
6123
6124 0.4091334550598e-08, 0.2452436180854e+01, 0.9779108567966e+01,
6125 0.3926694536146e-08, 0.6102292739040e+01, 0.1098419223922e+02,
6126 0.4841000253289e-08, 0.6072760457276e+01, 0.1252801878276e+02,
6127 0.4949340130240e-08, 0.1154832815171e+01, 0.1617106187867e+03,
6128 0.3761557737360e-08, 0.5527545321897e+01, 0.3185192151914e+01,
6129 0.3647396268188e-08, 0.1525035688629e+01, 0.6271346477544e+01,
6130 0.3932405074189e-08, 0.5570681040569e+01, 0.2139354194808e+02,
6131 0.3631322501141e-08, 0.1981240601160e+01, 0.6294805223347e+01,
6132 0.4130007425139e-08, 0.2050060880201e+01, 0.2195415756911e+02,
6133 0.4433905965176e-08, 0.3277477970321e+01, 0.7445550607224e+01,
6134
6135 0.3851814176947e-08, 0.5210690074886e+01, 0.9562891316684e+00,
6136 0.3485807052785e-08, 0.6653274904611e+00, 0.1161697602389e+02,
6137 0.3979772816991e-08, 0.1767941436148e+01, 0.2277943724828e+02,
6138 0.3402607460500e-08, 0.3421746306465e+01, 0.1087398597200e+02,
6139 0.4049993000926e-08, 0.1127144787547e+01, 0.3163918923335e+00,
6140 0.3420511182382e-08, 0.4214794779161e+01, 0.1362553364512e+02,
6141 0.3640772365012e-08, 0.5324905497687e+01, 0.1725304118033e+02,
6142 0.3323037987501e-08, 0.6135761838271e+01, 0.6279143387820e+01,
6143 0.4503141663637e-08, 0.1802305450666e+01, 0.1385561574497e+01,
6144 0.4314560055588e-08, 0.4812299731574e+01, 0.4176041334900e+01,
6145
6146 0.3294226949110e-08, 0.3657547059723e+01, 0.6287008313071e+01,
6147 0.3215657197281e-08, 0.4866676894425e+01, 0.5749861718712e+01,
6148 0.4129362656266e-08, 0.3809342558906e+01, 0.5905702259363e+01,
6149 0.3137762976388e-08, 0.2494635174443e+01, 0.2099539292909e+02,
6150 0.3514010952384e-08, 0.2699961831678e+01, 0.7335344340001e+01,
6151 0.3327607571530e-08, 0.3318457714816e+01, 0.5436992986000e+01,
6152 0.3541066946675e-08, 0.4382703582466e+01, 0.1234573916645e+02,
6153 0.3216179847052e-08, 0.5271066317054e+01, 0.3802769619140e-01,
6154 0.2959045059570e-08, 0.5819591585302e+01, 0.2670964694522e+02,
6155 0.3884040326665e-08, 0.5980934960428e+01, 0.6660449441528e+01,
6156
6157 0.2922027539886e-08, 0.3337290282483e+01, 0.1375773836557e+01,
6158 0.4110846382042e-08, 0.5742978187327e+01, 0.4480965020977e+02,
6159 0.2934508411032e-08, 0.2278075804200e+01, 0.6408777551755e+00,
6160 0.3966896193000e-08, 0.5835747858477e+01, 0.3773735910827e+00,
6161 0.3286695827610e-08, 0.5838898193902e+01, 0.3932462625300e-02,
6162 0.3720643094196e-08, 0.1122212337858e+01, 0.1646033343740e+02,
6163 0.3285508906174e-08, 0.9182250996416e+00, 0.1081813534213e+02,
6164 0.3753880575973e-08, 0.5174761973266e+01, 0.5642198095270e+01,
6165 0.3022129385587e-08, 0.3381611020639e+01, 0.2982630633589e+02,
6166 0.2798569205621e-08, 0.3546193723922e+01, 0.1937891852345e+02,
6167
6168 0.3397872070505e-08, 0.4533203197934e+01, 0.6923953605621e+01,
6169 0.3708099772977e-08, 0.2756168198616e+01, 0.3066615496545e+02,
6170 0.3599283541510e-08, 0.1934395469918e+01, 0.6147450479709e+01,
6171 0.3688702753059e-08, 0.7149920971109e+00, 0.2636725487657e+01,
6172 0.2681084724003e-08, 0.4899819493154e+01, 0.6816289982179e+01,
6173 0.3495993460759e-08, 0.1572418915115e+01, 0.6418701221183e+01,
6174 0.3130770324995e-08, 0.8912190180489e+00, 0.1235996607578e+02,
6175 0.2744353821941e-08, 0.3800821940055e+01, 0.2059724391010e+02,
6176 0.2842732906341e-08, 0.2644717440029e+01, 0.2828699048865e+02,
6177 0.3046882682154e-08, 0.3987793020179e+01, 0.6055599646783e+01,
6178
6179 0.2399072455143e-08, 0.9908826440764e+00, 0.6255674361143e+01,
6180 0.2384306274204e-08, 0.2516149752220e+01, 0.6310477339748e+01,
6181 0.2977324500559e-08, 0.5849195642118e+01, 0.1652265972112e+02,
6182 0.3062835258972e-08, 0.1681660100162e+01, 0.1172006883645e+02,
6183 0.3109682589231e-08, 0.5804143987737e+00, 0.2751146787858e+02,
6184 0.2903920355299e-08, 0.5800768280123e+01, 0.6510552054109e+01,
6185 0.2823221989212e-08, 0.9241118370216e+00, 0.5469525544182e+01,
6186 0.3187949696649e-08, 0.3139776445735e+01, 0.1693792562116e+03,
6187 0.2922559771655e-08, 0.3549440782984e+01, 0.2630839062450e+00,
6188 0.2436302066603e-08, 0.4735540696319e+01, 0.3946258593675e+00,
6189
6190 0.3049473043606e-08, 0.4998289124561e+01, 0.8390110365991e+01,
6191 0.2863682575784e-08, 0.6709515671102e+00, 0.2243449970715e+00,
6192 0.2641750517966e-08, 0.5410978257284e+01, 0.2986433403208e+02,
6193 0.2704093466243e-08, 0.4778317207821e+01, 0.6129297044991e+01,
6194 0.2445522177011e-08, 0.6009020662222e+01, 0.1171295538178e+02,
6195 0.2623608810230e-08, 0.5010449777147e+01, 0.6436854655901e+01,
6196 0.2079259704053e-08, 0.5980943768809e+01, 0.2019909489111e+02,
6197 0.2820225596771e-08, 0.2679965110468e+01, 0.5934151399930e+01,
6198 0.2365221950927e-08, 0.1894231148810e+01, 0.2470570524223e+02,
6199 0.2359682077149e-08, 0.4220752950780e+01, 0.8671969964381e+01,
6200
6201 0.2387577137206e-08, 0.2571783940617e+01, 0.7096626156709e+01,
6202 0.1982102089816e-08, 0.5169765997119e+00, 0.1727188400790e+02,
6203 0.2687502389925e-08, 0.6239078264579e+01, 0.7075506709219e+02,
6204 0.2207751669135e-08, 0.2031184412677e+01, 0.4377611041777e+01,
6205 0.2618370214274e-08, 0.8266079985979e+00, 0.6632000300961e+01,
6206 0.2591951887361e-08, 0.8819350522008e+00, 0.4873985990671e+02,
6207 0.2375055656248e-08, 0.3520944177789e+01, 0.1590676413561e+02,
6208 0.2472019978911e-08, 0.1551431908671e+01, 0.6612329252343e+00,
6209 0.2368157127199e-08, 0.4178610147412e+01, 0.3459636466239e+02,
6210 0.1764846605693e-08, 0.1506764000157e+01, 0.1980094587212e+02,
6211
6212 0.2291769608798e-08, 0.2118250611782e+01, 0.2844914056730e-01,
6213 0.2209997316943e-08, 0.3363255261678e+01, 0.2666070658668e+00,
6214 0.2292699097923e-08, 0.4200423956460e+00, 0.1484170571900e-02,
6215 0.1629683015329e-08, 0.2331362582487e+01, 0.3035599730800e+02,
6216 0.2206492862426e-08, 0.3400274026992e+01, 0.6281667977667e+01,
6217 0.2205746568257e-08, 0.1066051230724e+00, 0.6284483723224e+01,
6218 0.2026310767991e-08, 0.2779066487979e+01, 0.2449240616245e+02,
6219 0.1762977622163e-08, 0.9951450691840e+00, 0.2045286941806e+02,
6220 0.1368535049606e-08, 0.6402447365817e+00, 0.2473415438279e+02,
6221 0.1720598775450e-08, 0.2303524214705e+00, 0.1679593901136e+03,
6222
6223 0.1702429015449e-08, 0.6164622655048e+01, 0.3338575901272e+03,
6224 0.1414033197685e-08, 0.3954561185580e+01, 0.1624205518357e+03,
6225 0.1573768958043e-08, 0.2028286308984e+01, 0.3144167757552e+02,
6226 0.1650705184447e-08, 0.2304040666128e+01, 0.5267006960365e+02,
6227 0.1651087618855e-08, 0.2538461057280e+01, 0.8956999012000e+02,
6228 0.1616409518983e-08, 0.5111054348152e+01, 0.3332657872986e+02,
6229 0.1537175173581e-08, 0.5601130666603e+01, 0.3852657435933e+02,
6230 0.1593191980553e-08, 0.2614340453411e+01, 0.2282781046519e+03,
6231 0.1499480170643e-08, 0.3624721577264e+01, 0.2823723341956e+02,
6232 0.1493807843235e-08, 0.4214569879008e+01, 0.2876692439167e+02,
6233
6234 0.1074571199328e-08, 0.1496911744704e+00, 0.8397383534231e+02,
6235 0.1074406983417e-08, 0.1187817671922e+01, 0.8401985929482e+02,
6236 0.9757576855851e-09, 0.2655703035858e+01, 0.7826370942180e+02,
6237 0.1258432887565e-08, 0.4969896184844e+01, 0.3115650189215e+03,
6238 0.1240336343282e-08, 0.5192460776926e+01, 0.1784300471910e+03,
6239 0.9016107005164e-09, 0.1960356923057e+01, 0.5886454391678e+02,
6240 0.1135392360918e-08, 0.5082427809068e+01, 0.7842370451713e+02,
6241 0.9216046089565e-09, 0.2793775037273e+01, 0.1014262087719e+03,
6242 0.1061276615030e-08, 0.3726144311409e+01, 0.5660027930059e+02,
6243 0.1010110596263e-08, 0.7404080708937e+00, 0.4245678405627e+02,
6244
6245 0.7217424756199e-09, 0.2697449980577e-01, 0.2457074661053e+03,
6246 0.6912003846756e-09, 0.4253296276335e+01, 0.1679936946371e+03,
6247 0.6871814664847e-09, 0.5148072412354e+01, 0.6053048899753e+02,
6248 0.4887158016343e-09, 0.2153581148294e+01, 0.9656299901946e+02,
6249 0.5161802866314e-09, 0.3852750634351e+01, 0.2442876000072e+03,
6250 0.5652599559057e-09, 0.1233233356270e+01, 0.8365903305582e+02,
6251 0.4710812608586e-09, 0.5610486976767e+01, 0.3164282286739e+03,
6252 0.4909977500324e-09, 0.1639629524123e+01, 0.4059982187939e+03,
6253 0.4772641839378e-09, 0.3737100368583e+01, 0.1805255418145e+03,
6254 0.4487562567153e-09, 0.1158417054478e+00, 0.8433466158131e+02,
6255
6256 0.3943441230497e-09, 0.6243502862796e+00, 0.2568537517081e+03,
6257 0.3952236913598e-09, 0.3510377382385e+01, 0.2449975330562e+03,
6258 0.3788898363417e-09, 0.5916128302299e+01, 0.1568131045107e+03,
6259 0.3738329328831e-09, 0.1042266763456e+01, 0.3948519331910e+03,
6260 0.2451199165151e-09, 0.1166788435700e+01, 0.1435713242844e+03,
6261 0.2436734402904e-09, 0.3254726114901e+01, 0.2268582385539e+03,
6262 0.2213605274325e-09, 0.1687210598530e+01, 0.1658638954901e+03,
6263 0.1491521204829e-09, 0.2657541786794e+01, 0.2219950288015e+03,
6264 0.1474995329744e-09, 0.5013089805819e+01, 0.3052819430710e+03,
6265 0.1661939475656e-09, 0.5495315428418e+01, 0.2526661704812e+03,
6266
6267 0.9015946748003e-10, 0.2236989966505e+01, 0.4171445043968e+03 };
6268
6269 /* Sun-to-Earth, T^0, Z */
6270 static final double e0z[] = {
6271 0.2796207639075e-05, 0.3198701560209e+01, 0.8433466158131e+02,
6272 0.1016042198142e-05, 0.5422360395913e+01, 0.5507553240374e+01,
6273 0.8044305033647e-06, 0.3880222866652e+01, 0.5223693906222e+01,
6274 0.4385347909274e-06, 0.3704369937468e+01, 0.2352866153506e+01,
6275 0.3186156414906e-06, 0.3999639363235e+01, 0.1577343543434e+01,
6276 0.2272412285792e-06, 0.3984738315952e+01, 0.1047747311755e+01,
6277 0.1645620103007e-06, 0.3565412516841e+01, 0.5856477690889e+01,
6278 0.1815836921166e-06, 0.4984507059020e+01, 0.6283075850446e+01,
6279 0.1447461676364e-06, 0.3702753570108e+01, 0.9437762937313e+01,
6280 0.1430760876382e-06, 0.3409658712357e+01, 0.1021328554739e+02,
6281
6282 0.1120445753226e-06, 0.4829561570246e+01, 0.1414349524433e+02,
6283 0.1090232840797e-06, 0.2080729178066e+01, 0.6812766822558e+01,
6284 0.9715727346551e-07, 0.3476295881948e+01, 0.4694002934110e+01,
6285 0.1036267136217e-06, 0.4056639536648e+01, 0.7109288135493e+02,
6286 0.8752665271340e-07, 0.4448159519911e+01, 0.5753384878334e+01,
6287 0.8331864956004e-07, 0.4991704044208e+01, 0.7084896783808e+01,
6288 0.6901658670245e-07, 0.4325358994219e+01, 0.6275962395778e+01,
6289 0.9144536848998e-07, 0.1141826375363e+01, 0.6620890113188e+01,
6290 0.7205085037435e-07, 0.3624344170143e+01, 0.5296909721118e+00,
6291 0.7697874654176e-07, 0.5554257458998e+01, 0.1676215758509e+03,
6292
6293 0.5197545738384e-07, 0.6251760961735e+01, 0.1807370494127e+02,
6294 0.5031345378608e-07, 0.2497341091913e+01, 0.4705732307012e+01,
6295 0.4527110205840e-07, 0.2335079920992e+01, 0.6309374173736e+01,
6296 0.4753355798089e-07, 0.7094148987474e+00, 0.5884926831456e+01,
6297 0.4296951977516e-07, 0.1101916352091e+01, 0.6681224869435e+01,
6298 0.3855341568387e-07, 0.1825495405486e+01, 0.5486777812467e+01,
6299 0.5253930970990e-07, 0.4424740687208e+01, 0.7860419393880e+01,
6300 0.4024630496471e-07, 0.5120498157053e+01, 0.1336797263425e+02,
6301 0.4061069791453e-07, 0.6029771435451e+01, 0.3930209696940e+01,
6302 0.3797883804205e-07, 0.4435193600836e+00, 0.3154687086868e+01,
6303
6304 0.2933033225587e-07, 0.5124157356507e+01, 0.1059381944224e+01,
6305 0.3503000930426e-07, 0.5421830162065e+01, 0.6069776770667e+01,
6306 0.3670096214050e-07, 0.4582101667297e+01, 0.1219403291462e+02,
6307 0.2905609437008e-07, 0.1926566420072e+01, 0.1097707878456e+02,
6308 0.2466827821713e-07, 0.6090174539834e+00, 0.6496374930224e+01,
6309 0.2691647295332e-07, 0.1393432595077e+01, 0.2200391463820e+02,
6310 0.2150554667946e-07, 0.4308671715951e+01, 0.5643178611111e+01,
6311 0.2237481922680e-07, 0.8133968269414e+00, 0.8635942003952e+01,
6312 0.1817741038157e-07, 0.3755205127454e+01, 0.3340612434717e+01,
6313 0.2227820762132e-07, 0.2759558596664e+01, 0.1203646072878e+02,
6314
6315 0.1944713772307e-07, 0.5699645869121e+01, 0.1179062909082e+02,
6316 0.1527340520662e-07, 0.1986749091746e+01, 0.3981490189893e+00,
6317 0.1577282574914e-07, 0.3205017217983e+01, 0.5088628793478e+01,
6318 0.1424738825424e-07, 0.6256747903666e+01, 0.2544314396739e+01,
6319 0.1616563121701e-07, 0.2601671259394e+00, 0.1729818233119e+02,
6320 0.1401210391692e-07, 0.4686939173506e+01, 0.7058598460518e+01,
6321 0.1488726974214e-07, 0.2815862451372e+01, 0.2593412433514e+02,
6322 0.1692626442388e-07, 0.4956894109797e+01, 0.1564752902480e+03,
6323 0.1123571582910e-07, 0.2381192697696e+01, 0.3738761453707e+01,
6324 0.9903308606317e-08, 0.4294851657684e+01, 0.9225539266174e+01,
6325
6326 0.9174533187191e-08, 0.3075171510642e+01, 0.4164311961999e+01,
6327 0.8645985631457e-08, 0.5477534821633e+00, 0.8429241228195e+01,
6328 -0.1085876492688e-07, 0.0000000000000e+00, 0.0000000000000e+00,
6329 0.9264309077815e-08, 0.5968571670097e+01, 0.7079373888424e+01,
6330 0.8243116984954e-08, 0.1489098777643e+01, 0.1044738781244e+02,
6331 0.8268102113708e-08, 0.3512977691983e+01, 0.1150676975667e+02,
6332 0.9043613988227e-08, 0.1290704408221e+00, 0.1101510648075e+02,
6333 0.7432912038789e-08, 0.1991086893337e+01, 0.2608790314060e+02,
6334 0.8586233727285e-08, 0.4238357924414e+01, 0.2986433403208e+02,
6335 0.7612230060131e-08, 0.2911090150166e+01, 0.4732030630302e+01,
6336
6337 0.7097787751408e-08, 0.1908938392390e+01, 0.8031092209206e+01,
6338 0.7640237040175e-08, 0.6129219000168e+00, 0.7962980379786e+00,
6339 0.7070445688081e-08, 0.1380417036651e+01, 0.2146165377750e+01,
6340 0.7690770957702e-08, 0.1680504249084e+01, 0.2122839202813e+02,
6341 0.8051292542594e-08, 0.5127423484511e+01, 0.2942463415728e+01,
6342 0.5902709104515e-08, 0.2020274190917e+01, 0.7755226100720e+00,
6343 0.5134567496462e-08, 0.2606778676418e+01, 0.1256615170089e+02,
6344 0.5525802046102e-08, 0.1613011769663e+01, 0.8018209333619e+00,
6345 0.5880724784221e-08, 0.4604483417236e+01, 0.4690479774488e+01,
6346 0.5211699081370e-08, 0.5718964114193e+01, 0.8827390247185e+01,
6347
6348 0.4891849573562e-08, 0.3689658932196e+01, 0.2132990797783e+00,
6349 0.5150246069997e-08, 0.4099769855122e+01, 0.6480980550449e+02,
6350 0.5102434319633e-08, 0.5660834602509e+01, 0.3379454372902e+02,
6351 0.5083405254252e-08, 0.9842221218974e+00, 0.4136910472696e+01,
6352 0.4206562585682e-08, 0.1341363634163e+00, 0.3128388763578e+01,
6353 0.4663249683579e-08, 0.8130132735866e+00, 0.5216580451554e+01,
6354 0.4099474416530e-08, 0.5791497770644e+01, 0.4265981595566e+00,
6355 0.4628251220767e-08, 0.1249802769331e+01, 0.1572083878776e+02,
6356 0.5024068728142e-08, 0.4795684802743e+01, 0.6290189305114e+01,
6357 0.5120234327758e-08, 0.3810420387208e+01, 0.5230807360890e+01,
6358
6359 0.5524029815280e-08, 0.1029264714351e+01, 0.2397622045175e+03,
6360 0.4757415718860e-08, 0.3528044781779e+01, 0.1649636139783e+02,
6361 0.3915786131127e-08, 0.5593889282646e+01, 0.1589072916335e+01,
6362 0.4869053149991e-08, 0.3299636454433e+01, 0.7632943190217e+01,
6363 0.3649365703729e-08, 0.1286049002584e+01, 0.6206810014183e+01,
6364 0.3992493949002e-08, 0.3100307589464e+01, 0.2515860172507e+02,
6365 0.3320247477418e-08, 0.6212683940807e+01, 0.1216800268190e+02,
6366 0.3287123739696e-08, 0.4699118445928e+01, 0.7234794171227e+01,
6367 0.3472776811103e-08, 0.2630507142004e+01, 0.7342457794669e+01,
6368 0.3423253294767e-08, 0.2946432844305e+01, 0.9623688285163e+01,
6369
6370 0.3896173898244e-08, 0.1224834179264e+01, 0.6438496133249e+01,
6371 0.3388455337924e-08, 0.1543807616351e+01, 0.1494531617769e+02,
6372 0.3062704716523e-08, 0.1191777572310e+01, 0.8662240327241e+01,
6373 0.3270075600400e-08, 0.5483498767737e+01, 0.1194447056968e+01,
6374 0.3101209215259e-08, 0.8000833804348e+00, 0.3772475342596e+02,
6375 0.2780883347311e-08, 0.4077980721888e+00, 0.5863591145557e+01,
6376 0.2903605931824e-08, 0.2617490302147e+01, 0.1965104848470e+02,
6377 0.2682014743119e-08, 0.2634703158290e+01, 0.7238675589263e+01,
6378 0.2534360108492e-08, 0.6102446114873e+01, 0.6836645152238e+01,
6379 0.2392564882509e-08, 0.3681820208691e+01, 0.5849364236221e+01,
6380
6381 0.2656667254856e-08, 0.6216045388886e+01, 0.6133512519065e+01,
6382 0.2331242096773e-08, 0.5864949777744e+01, 0.4535059491685e+01,
6383 0.2287898363668e-08, 0.4566628532802e+01, 0.7477522907414e+01,
6384 0.2336944521306e-08, 0.2442722126930e+01, 0.1137170464392e+02,
6385 0.3156632236269e-08, 0.1626628050682e+01, 0.2509084901204e+03,
6386 0.2982612402766e-08, 0.2803604512609e+01, 0.1748016358760e+01,
6387 0.2774031674807e-08, 0.4654002897158e+01, 0.8223916695780e+02,
6388 0.2295236548638e-08, 0.4326518333253e+01, 0.3378142627421e+00,
6389 0.2190714699873e-08, 0.4519614578328e+01, 0.2908881142201e+02,
6390 0.2191495845045e-08, 0.3012626912549e+01, 0.1673046366289e+02,
6391
6392 0.2492901628386e-08, 0.1290101424052e+00, 0.1543797956245e+03,
6393 0.1993778064319e-08, 0.3864046799414e+01, 0.1778984560711e+02,
6394 0.1898146479022e-08, 0.5053777235891e+01, 0.2042657109477e+02,
6395 0.1918280127634e-08, 0.2222470192548e+01, 0.4165496312290e+02,
6396 0.1916351061607e-08, 0.8719067257774e+00, 0.7737595720538e+02,
6397 0.1834720181466e-08, 0.4031491098040e+01, 0.2358125818164e+02,
6398 0.1249201523806e-08, 0.5938379466835e+01, 0.3301902111895e+02,
6399 0.1477304050539e-08, 0.6544722606797e+00, 0.9548094718417e+02,
6400 0.1264316431249e-08, 0.2059072853236e+01, 0.8399684731857e+02,
6401 0.1203526495039e-08, 0.3644813532605e+01, 0.4558517281984e+02,
6402
6403 0.9221681059831e-09, 0.3241815055602e+01, 0.7805158573086e+02,
6404 0.7849278367646e-09, 0.5043812342457e+01, 0.5217580628120e+02,
6405 0.7983392077387e-09, 0.5000024502753e+01, 0.1501922143975e+03,
6406 0.7925395431654e-09, 0.1398734871821e-01, 0.9061773743175e+02,
6407 0.7640473285886e-09, 0.5067111723130e+01, 0.4951538251678e+02,
6408 0.5398937754482e-09, 0.5597382200075e+01, 0.1613385000004e+03,
6409 0.5626247550193e-09, 0.2601338209422e+01, 0.7318837597844e+02,
6410 0.5525197197855e-09, 0.5814832109256e+01, 0.1432335100216e+03,
6411 0.5407629837898e-09, 0.3384820609076e+01, 0.3230491187871e+03,
6412 0.3856739119801e-09, 0.1072391840473e+01, 0.2334791286671e+03,
6413
6414 0.3856425239987e-09, 0.2369540393327e+01, 0.1739046517013e+03,
6415 0.4350867755983e-09, 0.5255575751082e+01, 0.1620484330494e+03,
6416 0.3844113924996e-09, 0.5482356246182e+01, 0.9757644180768e+02,
6417 0.2854869155431e-09, 0.9573634763143e+00, 0.1697170704744e+03,
6418 0.1719227671416e-09, 0.1887203025202e+01, 0.2265204242912e+03,
6419 0.1527846879755e-09, 0.3982183931157e+01, 0.3341954043900e+03,
6420 0.1128229264847e-09, 0.2787457156298e+01, 0.3119028331842e+03 };
6421
6422 /* Sun-to-Earth, T^1, X */
6423 static final double e1x[] = {
6424 0.1234046326004e-05, 0.0000000000000e+00, 0.0000000000000e+00,
6425 0.5150068824701e-06, 0.6002664557501e+01, 0.1256615170089e+02,
6426 0.1290743923245e-07, 0.5959437664199e+01, 0.1884922755134e+02,
6427 0.1068615564952e-07, 0.2015529654209e+01, 0.6283075850446e+01,
6428 0.2079619142538e-08, 0.1732960531432e+01, 0.6279552690824e+01,
6429 0.2078009243969e-08, 0.4915604476996e+01, 0.6286599010068e+01,
6430 0.6206330058856e-09, 0.3616457953824e+00, 0.4705732307012e+01,
6431 0.5989335313746e-09, 0.3802607304474e+01, 0.6256777527156e+01,
6432 0.5958495663840e-09, 0.2845866560031e+01, 0.6309374173736e+01,
6433 0.4866923261539e-09, 0.5213203771824e+01, 0.7755226100720e+00,
6434
6435 0.4267785823142e-09, 0.4368189727818e+00, 0.1059381944224e+01,
6436 0.4610675141648e-09, 0.1837249181372e-01, 0.7860419393880e+01,
6437 0.3626989993973e-09, 0.2161590545326e+01, 0.5753384878334e+01,
6438 0.3563071194389e-09, 0.1452631954746e+01, 0.5884926831456e+01,
6439 0.3557015642807e-09, 0.4470593393054e+01, 0.6812766822558e+01,
6440 0.3210412089122e-09, 0.5195926078314e+01, 0.6681224869435e+01,
6441 0.2875473577986e-09, 0.5916256610193e+01, 0.2513230340178e+02,
6442 0.2842913681629e-09, 0.1149902426047e+01, 0.6127655567643e+01,
6443 0.2751248215916e-09, 0.5502088574662e+01, 0.6438496133249e+01,
6444 0.2481432881127e-09, 0.2921989846637e+01, 0.5486777812467e+01,
6445
6446 0.2059885976560e-09, 0.3718070376585e+01, 0.7079373888424e+01,
6447 0.2015522342591e-09, 0.5979395259740e+01, 0.6290189305114e+01,
6448 0.1995364084253e-09, 0.6772087985494e+00, 0.6275962395778e+01,
6449 0.1957436436943e-09, 0.2899210654665e+01, 0.5507553240374e+01,
6450 0.1651609818948e-09, 0.6228206482192e+01, 0.1150676975667e+02,
6451 0.1822980550699e-09, 0.1469348746179e+01, 0.1179062909082e+02,
6452 0.1675223159760e-09, 0.3813910555688e+01, 0.7058598460518e+01,
6453 0.1706491764745e-09, 0.3004380506684e+00, 0.7113454667900e-02,
6454 0.1392952362615e-09, 0.1440393973406e+01, 0.7962980379786e+00,
6455 0.1209868266342e-09, 0.4150425791727e+01, 0.4694002934110e+01,
6456
6457 0.1009827202611e-09, 0.3290040429843e+01, 0.3738761453707e+01,
6458 0.1047261388602e-09, 0.4229590090227e+01, 0.6282095334605e+01,
6459 0.1047006652004e-09, 0.2418967680575e+01, 0.6284056366286e+01,
6460 0.9609993143095e-10, 0.4627943659201e+01, 0.6069776770667e+01,
6461 0.9590900593873e-10, 0.1894393939924e+01, 0.4136910472696e+01,
6462 0.9146249188071e-10, 0.2010647519562e+01, 0.6496374930224e+01,
6463 0.8545274480290e-10, 0.5529846956226e-01, 0.1194447056968e+01,
6464 0.8224377881194e-10, 0.1254304102174e+01, 0.1589072916335e+01,
6465 0.6183529510410e-10, 0.3360862168815e+01, 0.8827390247185e+01,
6466 0.6259255147141e-10, 0.4755628243179e+01, 0.8429241228195e+01,
6467
6468 0.5539291694151e-10, 0.5371746955142e+01, 0.4933208510675e+01,
6469 0.7328259466314e-10, 0.4927699613906e+00, 0.4535059491685e+01,
6470 0.6017835843560e-10, 0.5776682001734e-01, 0.1255903824622e+02,
6471 0.7079827775243e-10, 0.4395059432251e+01, 0.5088628793478e+01,
6472 0.5170358878213e-10, 0.5154062619954e+01, 0.1176985366291e+02,
6473 0.4872301838682e-10, 0.6289611648973e+00, 0.6040347114260e+01,
6474 0.5249869411058e-10, 0.5617272046949e+01, 0.3154687086868e+01,
6475 0.4716172354411e-10, 0.3965901800877e+01, 0.5331357529664e+01,
6476 0.4871214940964e-10, 0.4627507050093e+01, 0.1256967486051e+02,
6477 0.4598076850751e-10, 0.6023631226459e+01, 0.6525804586632e+01,
6478
6479 0.4562196089485e-10, 0.4138562084068e+01, 0.3930209696940e+01,
6480 0.4325493872224e-10, 0.1330845906564e+01, 0.7632943190217e+01,
6481 0.5673781176748e-10, 0.2558752615657e+01, 0.5729506548653e+01,
6482 0.3961436642503e-10, 0.2728071734630e+01, 0.7234794171227e+01,
6483 0.5101868209058e-10, 0.4113444965144e+01, 0.6836645152238e+01,
6484 0.5257043167676e-10, 0.6195089830590e+01, 0.8031092209206e+01,
6485 0.5076613989393e-10, 0.2305124132918e+01, 0.7477522907414e+01,
6486 0.3342169352778e-10, 0.5415998155071e+01, 0.1097707878456e+02,
6487 0.3545881983591e-10, 0.3727160564574e+01, 0.4164311961999e+01,
6488 0.3364063738599e-10, 0.2901121049204e+00, 0.1137170464392e+02,
6489
6490 0.3357039670776e-10, 0.1652229354331e+01, 0.5223693906222e+01,
6491 0.4307412268687e-10, 0.4938909587445e+01, 0.1592596075957e+01,
6492 0.3405769115435e-10, 0.2408890766511e+01, 0.3128388763578e+01,
6493 0.3001926198480e-10, 0.4862239006386e+01, 0.1748016358760e+01,
6494 0.2778264787325e-10, 0.5241168661353e+01, 0.7342457794669e+01,
6495 0.2676159480666e-10, 0.3423593942199e+01, 0.2146165377750e+01,
6496 0.2954273399939e-10, 0.1881721265406e+01, 0.5368044267797e+00,
6497 0.3309362888795e-10, 0.1931525677349e+01, 0.8018209333619e+00,
6498 0.2810283608438e-10, 0.2414659495050e+01, 0.5225775174439e+00,
6499 0.3378045637764e-10, 0.4238019163430e+01, 0.1554202828031e+00,
6500
6501 0.2558134979840e-10, 0.1828225235805e+01, 0.5230807360890e+01,
6502 0.2273755578447e-10, 0.5858184283998e+01, 0.7084896783808e+01,
6503 0.2294176037690e-10, 0.4514589779057e+01, 0.1726015463500e+02,
6504 0.2533506099435e-10, 0.2355717851551e+01, 0.5216580451554e+01,
6505 0.2716685375812e-10, 0.2221003625100e+01, 0.8635942003952e+01,
6506 0.2419043435198e-10, 0.5955704951635e+01, 0.4690479774488e+01,
6507 0.2521232544812e-10, 0.1395676848521e+01, 0.5481254917084e+01,
6508 0.2630195021491e-10, 0.5727468918743e+01, 0.2629832328990e-01,
6509 0.2548395840944e-10, 0.2628351859400e-03, 0.1349867339771e+01 };
6510
6511 /* Sun-to-Earth, T^1, Y */
6512 static final double e1y[] = {
6513 0.9304690546528e-06, 0.0000000000000e+00, 0.0000000000000e+00,
6514 0.5150715570663e-06, 0.4431807116294e+01, 0.1256615170089e+02,
6515 0.1290825411056e-07, 0.4388610039678e+01, 0.1884922755134e+02,
6516 0.4645466665386e-08, 0.5827263376034e+01, 0.6283075850446e+01,
6517 0.2079625310718e-08, 0.1621698662282e+00, 0.6279552690824e+01,
6518 0.2078189850907e-08, 0.3344713435140e+01, 0.6286599010068e+01,
6519 0.6207190138027e-09, 0.5074049319576e+01, 0.4705732307012e+01,
6520 0.5989826532569e-09, 0.2231842216620e+01, 0.6256777527156e+01,
6521 0.5961360812618e-09, 0.1274975769045e+01, 0.6309374173736e+01,
6522 0.4874165471016e-09, 0.3642277426779e+01, 0.7755226100720e+00,
6523
6524 0.4283834034360e-09, 0.5148765510106e+01, 0.1059381944224e+01,
6525 0.4652389287529e-09, 0.4715794792175e+01, 0.7860419393880e+01,
6526 0.3751707476401e-09, 0.6617207370325e+00, 0.5753384878334e+01,
6527 0.3559998806198e-09, 0.6155548875404e+01, 0.5884926831456e+01,
6528 0.3558447558857e-09, 0.2898827297664e+01, 0.6812766822558e+01,
6529 0.3211116927106e-09, 0.3625813502509e+01, 0.6681224869435e+01,
6530 0.2875609914672e-09, 0.4345435813134e+01, 0.2513230340178e+02,
6531 0.2843109704069e-09, 0.5862263940038e+01, 0.6127655567643e+01,
6532 0.2744676468427e-09, 0.3926419475089e+01, 0.6438496133249e+01,
6533 0.2481285237789e-09, 0.1351976572828e+01, 0.5486777812467e+01,
6534
6535 0.2060338481033e-09, 0.2147556998591e+01, 0.7079373888424e+01,
6536 0.2015822358331e-09, 0.4408358972216e+01, 0.6290189305114e+01,
6537 0.2001195944195e-09, 0.5385829822531e+01, 0.6275962395778e+01,
6538 0.1953667642377e-09, 0.1304933746120e+01, 0.5507553240374e+01,
6539 0.1839744078713e-09, 0.6173567228835e+01, 0.1179062909082e+02,
6540 0.1643334294845e-09, 0.4635942997523e+01, 0.1150676975667e+02,
6541 0.1768051018652e-09, 0.5086283558874e+01, 0.7113454667900e-02,
6542 0.1674874205489e-09, 0.2243332137241e+01, 0.7058598460518e+01,
6543 0.1421445397609e-09, 0.6186899771515e+01, 0.7962980379786e+00,
6544 0.1255163958267e-09, 0.5730238465658e+01, 0.4694002934110e+01,
6545
6546 0.1013945281961e-09, 0.1726055228402e+01, 0.3738761453707e+01,
6547 0.1047294335852e-09, 0.2658801228129e+01, 0.6282095334605e+01,
6548 0.1047103879392e-09, 0.8481047835035e+00, 0.6284056366286e+01,
6549 0.9530343962826e-10, 0.3079267149859e+01, 0.6069776770667e+01,
6550 0.9604637611690e-10, 0.3258679792918e+00, 0.4136910472696e+01,
6551 0.9153518537177e-10, 0.4398599886584e+00, 0.6496374930224e+01,
6552 0.8562458214922e-10, 0.4772686794145e+01, 0.1194447056968e+01,
6553 0.8232525360654e-10, 0.5966220721679e+01, 0.1589072916335e+01,
6554 0.6150223411438e-10, 0.1780985591923e+01, 0.8827390247185e+01,
6555 0.6272087858000e-10, 0.3184305429012e+01, 0.8429241228195e+01,
6556
6557 0.5540476311040e-10, 0.3801260595433e+01, 0.4933208510675e+01,
6558 0.7331901699361e-10, 0.5205948591865e+01, 0.4535059491685e+01,
6559 0.6018528702791e-10, 0.4770139083623e+01, 0.1255903824622e+02,
6560 0.5150530724804e-10, 0.3574796899585e+01, 0.1176985366291e+02,
6561 0.6471933741811e-10, 0.2679787266521e+01, 0.5088628793478e+01,
6562 0.5317460644174e-10, 0.9528763345494e+00, 0.3154687086868e+01,
6563 0.4832187748783e-10, 0.5329322498232e+01, 0.6040347114260e+01,
6564 0.4716763555110e-10, 0.2395235316466e+01, 0.5331357529664e+01,
6565 0.4871509139861e-10, 0.3056663648823e+01, 0.1256967486051e+02,
6566 0.4598417696768e-10, 0.4452762609019e+01, 0.6525804586632e+01,
6567
6568 0.5674189533175e-10, 0.9879680872193e+00, 0.5729506548653e+01,
6569 0.4073560328195e-10, 0.5939127696986e+01, 0.7632943190217e+01,
6570 0.5040994945359e-10, 0.4549875824510e+01, 0.8031092209206e+01,
6571 0.5078185134679e-10, 0.7346659893982e+00, 0.7477522907414e+01,
6572 0.3769343537061e-10, 0.1071317188367e+01, 0.7234794171227e+01,
6573 0.4980331365299e-10, 0.2500345341784e+01, 0.6836645152238e+01,
6574 0.3458236594757e-10, 0.3825159450711e+01, 0.1097707878456e+02,
6575 0.3578859493602e-10, 0.5299664791549e+01, 0.4164311961999e+01,
6576 0.3370504646419e-10, 0.5002316301593e+01, 0.1137170464392e+02,
6577 0.3299873338428e-10, 0.2526123275282e+01, 0.3930209696940e+01,
6578
6579 0.4304917318409e-10, 0.3368078557132e+01, 0.1592596075957e+01,
6580 0.3402418753455e-10, 0.8385495425800e+00, 0.3128388763578e+01,
6581 0.2778460572146e-10, 0.3669905203240e+01, 0.7342457794669e+01,
6582 0.2782710128902e-10, 0.2691664812170e+00, 0.1748016358760e+01,
6583 0.2711725179646e-10, 0.4707487217718e+01, 0.5296909721118e+00,
6584 0.2981760946340e-10, 0.3190260867816e+00, 0.5368044267797e+00,
6585 0.2811672977772e-10, 0.3196532315372e+01, 0.7084896783808e+01,
6586 0.2863454474467e-10, 0.2263240324780e+00, 0.5223693906222e+01,
6587 0.3333464634051e-10, 0.3498451685065e+01, 0.8018209333619e+00,
6588 0.3312991747609e-10, 0.5839154477412e+01, 0.1554202828031e+00,
6589
6590 0.2813255564006e-10, 0.8268044346621e+00, 0.5225775174439e+00,
6591 0.2665098083966e-10, 0.3934021725360e+01, 0.5216580451554e+01,
6592 0.2349795705216e-10, 0.5197620913779e+01, 0.2146165377750e+01,
6593 0.2330352293961e-10, 0.2984999231807e+01, 0.1726015463500e+02,
6594 0.2728001683419e-10, 0.6521679638544e+00, 0.8635942003952e+01,
6595 0.2484061007669e-10, 0.3468955561097e+01, 0.5230807360890e+01,
6596 0.2646328768427e-10, 0.1013724533516e+01, 0.2629832328990e-01,
6597 0.2518630264831e-10, 0.6108081057122e+01, 0.5481254917084e+01,
6598 0.2421901455384e-10, 0.1651097776260e+01, 0.1349867339771e+01,
6599 0.6348533267831e-11, 0.3220226560321e+01, 0.8433466158131e+02 };
6600
6601 /* Sun-to-Earth, T^1, Z */
6602 static final double e1z[] = {
6603 0.2278290449966e-05, 0.3413716033863e+01, 0.6283075850446e+01,
6604 0.5429458209830e-07, 0.0000000000000e+00, 0.0000000000000e+00,
6605 0.1903240492525e-07, 0.3370592358297e+01, 0.1256615170089e+02,
6606 0.2385409276743e-09, 0.3327914718416e+01, 0.1884922755134e+02,
6607 0.8676928342573e-10, 0.1824006811264e+01, 0.5223693906222e+01,
6608 0.7765442593544e-10, 0.3888564279247e+01, 0.5507553240374e+01,
6609 0.7066158332715e-10, 0.5194267231944e+01, 0.2352866153506e+01,
6610 0.7092175288657e-10, 0.2333246960021e+01, 0.8399684731857e+02,
6611 0.5357582213535e-10, 0.2224031176619e+01, 0.5296909721118e+00,
6612 0.3828035865021e-10, 0.2156710933584e+01, 0.6279552690824e+01,
6613
6614 0.3824857220427e-10, 0.1529755219915e+01, 0.6286599010068e+01,
6615 0.3286995181628e-10, 0.4879512900483e+01, 0.1021328554739e+02 };
6616
6617 /* Sun-to-Earth, T^2, X */
6618 static final double e2x[] = {
6619 -0.4143818297913e-10, 0.0000000000000e+00, 0.0000000000000e+00,
6620 0.2171497694435e-10, 0.4398225628264e+01, 0.1256615170089e+02,
6621 0.9845398442516e-11, 0.2079720838384e+00, 0.6283075850446e+01,
6622 0.9256833552682e-12, 0.4191264694361e+01, 0.1884922755134e+02,
6623 0.1022049384115e-12, 0.5381133195658e+01, 0.8399684731857e+02 };
6624
6625 /* Sun-to-Earth, T^2, Y */
6626 static final double e2y[] = {
6627 0.5063375872532e-10, 0.0000000000000e+00, 0.0000000000000e+00,
6628 0.2173815785980e-10, 0.2827805833053e+01, 0.1256615170089e+02,
6629 0.1010231999920e-10, 0.4634612377133e+01, 0.6283075850446e+01,
6630 0.9259745317636e-12, 0.2620612076189e+01, 0.1884922755134e+02,
6631 0.1022202095812e-12, 0.3809562326066e+01, 0.8399684731857e+02 };
6632
6633 /* Sun-to-Earth, T^2, Z */
6634 static final double e2z[] = {
6635 0.9722666114891e-10, 0.5152219582658e+01, 0.6283075850446e+01,
6636 -0.3494819171909e-11, 0.0000000000000e+00, 0.0000000000000e+00,
6637 0.6713034376076e-12, 0.6440188750495e+00, 0.1256615170089e+02 };
6638
6639 }
6640 //subclassed the
6641 private static class SSB {
6642 /* SSB-to-Sun, T^0, X */
6643 static final double s0x[] = {
6644 0.4956757536410e-02, 0.3741073751789e+01, 0.5296909721118e+00,
6645 0.2718490072522e-02, 0.4016011511425e+01, 0.2132990797783e+00,
6646 0.1546493974344e-02, 0.2170528330642e+01, 0.3813291813120e-01,
6647 0.8366855276341e-03, 0.2339614075294e+01, 0.7478166569050e-01,
6648 0.2936777942117e-03, 0.0000000000000e+00, 0.0000000000000e+00,
6649 0.1201317439469e-03, 0.4090736353305e+01, 0.1059381944224e+01,
6650 0.7578550887230e-04, 0.3241518088140e+01, 0.4265981595566e+00,
6651 0.1941787367773e-04, 0.1012202064330e+01, 0.2061856251104e+00,
6652 0.1889227765991e-04, 0.3892520416440e+01, 0.2204125344462e+00,
6653 0.1937896968613e-04, 0.4797779441161e+01, 0.1495633313810e+00,
6654
6655 0.1434506110873e-04, 0.3868960697933e+01, 0.5225775174439e+00,
6656 0.1406659911580e-04, 0.4759766557397e+00, 0.5368044267797e+00,
6657 0.1179022300202e-04, 0.7774961520598e+00, 0.7626583626240e-01,
6658 0.8085864460959e-05, 0.3254654471465e+01, 0.3664874755930e-01,
6659 0.7622752967615e-05, 0.4227633103489e+01, 0.3961708870310e-01,
6660 0.6209171139066e-05, 0.2791828325711e+00, 0.7329749511860e-01,
6661 0.4366435633970e-05, 0.4440454875925e+01, 0.1589072916335e+01,
6662 0.3792124889348e-05, 0.5156393842356e+01, 0.7113454667900e-02,
6663 0.3154548963402e-05, 0.6157005730093e+01, 0.4194847048887e+00,
6664 0.3088359882942e-05, 0.2494567553163e+01, 0.6398972393349e+00,
6665
6666 0.2788440902136e-05, 0.4934318747989e+01, 0.1102062672231e+00,
6667 0.3039928456376e-05, 0.4895077702640e+01, 0.6283075850446e+01,
6668 0.2272258457679e-05, 0.5278394064764e+01, 0.1030928125552e+00,
6669 0.2162007057957e-05, 0.5802978019099e+01, 0.3163918923335e+00,
6670 0.1767632855737e-05, 0.3415346595193e-01, 0.1021328554739e+02,
6671 0.1349413459362e-05, 0.2001643230755e+01, 0.1484170571900e-02,
6672 0.1170141900476e-05, 0.2424750491620e+01, 0.6327837846670e+00,
6673 0.1054355266820e-05, 0.3123311487576e+01, 0.4337116142245e+00,
6674 0.9800822461610e-06, 0.3026258088130e+01, 0.1052268489556e+01,
6675 0.1091203749931e-05, 0.3157811670347e+01, 0.1162474756779e+01,
6676
6677 0.6960236715913e-06, 0.8219570542313e+00, 0.1066495398892e+01,
6678 0.5689257296909e-06, 0.1323052375236e+01, 0.9491756770005e+00,
6679 0.6613172135802e-06, 0.2765348881598e+00, 0.8460828644453e+00,
6680 0.6277702517571e-06, 0.5794064466382e+01, 0.1480791608091e+00,
6681 0.6304884066699e-06, 0.7323555380787e+00, 0.2243449970715e+00,
6682 0.4897850467382e-06, 0.3062464235399e+01, 0.3340612434717e+01,
6683 0.3759148598786e-06, 0.4588290469664e+01, 0.3516457698740e-01,
6684 0.3110520548195e-06, 0.1374299536572e+01, 0.6373574839730e-01,
6685 0.3064708359780e-06, 0.4222267485047e+01, 0.1104591729320e-01,
6686 0.2856347168241e-06, 0.3714202944973e+01, 0.1510475019529e+00,
6687
6688 0.2840945514288e-06, 0.2847972875882e+01, 0.4110125927500e-01,
6689 0.2378951599405e-06, 0.3762072563388e+01, 0.2275259891141e+00,
6690 0.2714229481417e-06, 0.1036049980031e+01, 0.2535050500000e-01,
6691 0.2323551717307e-06, 0.4682388599076e+00, 0.8582758298370e-01,
6692 0.1881790512219e-06, 0.4790565425418e+01, 0.2118763888447e+01,
6693 0.2261353968371e-06, 0.1669144912212e+01, 0.7181332454670e-01,
6694 0.2214546389848e-06, 0.3937717281614e+01, 0.2968341143800e-02,
6695 0.2184915594933e-06, 0.1129169845099e+00, 0.7775000683430e-01,
6696 0.2000164937936e-06, 0.4030009638488e+01, 0.2093666171530e+00,
6697 0.1966105136719e-06, 0.8745955786834e+00, 0.2172315424036e+00,
6698
6699 0.1904742332624e-06, 0.5919743598964e+01, 0.2022531624851e+00,
6700 0.1657399705031e-06, 0.2549141484884e+01, 0.7358765972222e+00,
6701 0.1574070533987e-06, 0.5277533020230e+01, 0.7429900518901e+00,
6702 0.1832261651039e-06, 0.3064688127777e+01, 0.3235053470014e+00,
6703 0.1733615346569e-06, 0.3011432799094e+01, 0.1385174140878e+00,
6704 0.1549124014496e-06, 0.4005569132359e+01, 0.5154640627760e+00,
6705 0.1637044713838e-06, 0.1831375966632e+01, 0.8531963191132e+00,
6706 0.1123420082383e-06, 0.1180270407578e+01, 0.1990721704425e+00,
6707 0.1083754165740e-06, 0.3414101320863e+00, 0.5439178814476e+00,
6708 0.1156638012655e-06, 0.6130479452594e+00, 0.5257585094865e+00,
6709
6710 0.1142548785134e-06, 0.3724761948846e+01, 0.5336234347371e+00,
6711 0.7921463895965e-07, 0.2435425589361e+01, 0.1478866649112e+01,
6712 0.7428600285231e-07, 0.3542144398753e+01, 0.2164800718209e+00,
6713 0.8323211246747e-07, 0.3525058072354e+01, 0.1692165728891e+01,
6714 0.7257595116312e-07, 0.1364299431982e+01, 0.2101180877357e+00,
6715 0.7111185833236e-07, 0.2460478875808e+01, 0.4155522422634e+00,
6716 0.6868090383716e-07, 0.4397327670704e+01, 0.1173197218910e+00,
6717 0.7226419974175e-07, 0.4042647308905e+01, 0.1265567569334e+01,
6718 0.6955642383177e-07, 0.2865047906085e+01, 0.9562891316684e+00,
6719 0.7492139296331e-07, 0.5014278994215e+01, 0.1422690933580e-01,
6720
6721 0.6598363128857e-07, 0.2376730020492e+01, 0.6470106940028e+00,
6722 0.7381147293385e-07, 0.3272990384244e+01, 0.1581959461667e+01,
6723 0.6402909624032e-07, 0.5302290955138e+01, 0.9597935788730e-01,
6724 0.6237454263857e-07, 0.5444144425332e+01, 0.7084920306520e-01,
6725 0.5241198544016e-07, 0.4215359579205e+01, 0.5265099800692e+00,
6726 0.5144463853918e-07, 0.1218916689916e+00, 0.5328719641544e+00,
6727 0.5868164772299e-07, 0.2369402002213e+01, 0.7871412831580e-01,
6728 0.6233195669151e-07, 0.1254922242403e+01, 0.2608790314060e+02,
6729 0.6068463791422e-07, 0.5679713760431e+01, 0.1114304132498e+00,
6730 0.4359361135065e-07, 0.6097219641646e+00, 0.1375773836557e+01,
6731
6732 0.4686510366826e-07, 0.4786231041431e+01, 0.1143987543936e+00,
6733 0.3758977287225e-07, 0.1167368068139e+01, 0.1596186371003e+01,
6734 0.4282051974778e-07, 0.1519471064319e+01, 0.2770348281756e+00,
6735 0.5153765386113e-07, 0.1860532322984e+01, 0.2228608264996e+00,
6736 0.4575129387188e-07, 0.7632857887158e+00, 0.1465949902372e+00,
6737 0.3326844933286e-07, 0.1298219485285e+01, 0.5070101000000e-01,
6738 0.3748617450984e-07, 0.1046510321062e+01, 0.4903339079539e+00,
6739 0.2816756661499e-07, 0.3434522346190e+01, 0.2991266627620e+00,
6740 0.3412750405039e-07, 0.2523766270318e+01, 0.3518164938661e+00,
6741 0.2655796761776e-07, 0.2904422260194e+01, 0.6256703299991e+00,
6742
6743 0.2963597929458e-07, 0.5923900431149e+00, 0.1099462426779e+00,
6744 0.2539523734781e-07, 0.4851947722567e+01, 0.1256615170089e+02,
6745 0.2283087914139e-07, 0.3400498595496e+01, 0.6681224869435e+01,
6746 0.2321309799331e-07, 0.5789099148673e+01, 0.3368040641550e-01,
6747 0.2549657649750e-07, 0.3991856479792e-01, 0.1169588211447e+01,
6748 0.2290462303977e-07, 0.2788567577052e+01, 0.1045155034888e+01,
6749 0.1945398522914e-07, 0.3290896998176e+01, 0.1155361302111e+01,
6750 0.1849171512638e-07, 0.2698060129367e+01, 0.4452511715700e-02,
6751 0.1647199834254e-07, 0.3016735644085e+01, 0.4408250688924e+00,
6752 0.1529530765273e-07, 0.5573043116178e+01, 0.6521991896920e-01,
6753
6754 0.1433199339978e-07, 0.1481192356147e+01, 0.9420622223326e+00,
6755 0.1729134193602e-07, 0.1422817538933e+01, 0.2108507877249e+00,
6756 0.1716463931346e-07, 0.3469468901855e+01, 0.2157473718317e+00,
6757 0.1391206061378e-07, 0.6122436220547e+01, 0.4123712502208e+00,
6758 0.1404746661924e-07, 0.1647765641936e+01, 0.4258542984690e-01,
6759 0.1410452399455e-07, 0.5989729161964e+01, 0.2258291676434e+00,
6760 0.1089828772168e-07, 0.2833705509371e+01, 0.4226656969313e+00,
6761 0.1047374564948e-07, 0.5090690007331e+00, 0.3092784376656e+00,
6762 0.1358279126532e-07, 0.5128990262836e+01, 0.7923417740620e-01,
6763 0.1020456476148e-07, 0.9632772880808e+00, 0.1456308687557e+00,
6764
6765 0.1033428735328e-07, 0.3223779318418e+01, 0.1795258541446e+01,
6766 0.1412435841540e-07, 0.2410271572721e+01, 0.1525316725248e+00,
6767 0.9722759371574e-08, 0.2333531395690e+01, 0.8434341241180e-01,
6768 0.9657334084704e-08, 0.6199270974168e+01, 0.1272681024002e+01,
6769 0.1083641148690e-07, 0.2864222292929e+01, 0.7032915397480e-01,
6770 0.1067318403838e-07, 0.5833458866568e+00, 0.2123349582968e+00,
6771 0.1062366201976e-07, 0.4307753989494e+01, 0.2142632012598e+00,
6772 0.1236364149266e-07, 0.2873917870593e+01, 0.1847279083684e+00,
6773 0.1092759489593e-07, 0.2959887266733e+01, 0.1370332435159e+00,
6774 0.8912069362899e-08, 0.5141213702562e+01, 0.2648454860559e+01,
6775
6776 0.9656467707970e-08, 0.4532182462323e+01, 0.4376440768498e+00,
6777 0.8098386150135e-08, 0.2268906338379e+01, 0.2880807454688e+00,
6778 0.7857714675000e-08, 0.4055544260745e+01, 0.2037373330570e+00,
6779 0.7288455940646e-08, 0.5357901655142e+01, 0.1129145838217e+00,
6780 0.9450595950552e-08, 0.4264926963939e+01, 0.5272426800584e+00,
6781 0.9381718247537e-08, 0.7489366976576e-01, 0.5321392641652e+00,
6782 0.7079052646038e-08, 0.1923311052874e+01, 0.6288513220417e+00,
6783 0.9259004415344e-08, 0.2970256853438e+01, 0.1606092486742e+00,
6784 0.8259801499742e-08, 0.3327056314697e+01, 0.8389694097774e+00,
6785 0.6476334355779e-08, 0.2954925505727e+01, 0.2008557621224e+01,
6786
6787 0.5984021492007e-08, 0.9138753105829e+00, 0.2042657109477e+02,
6788 0.5989546863181e-08, 0.3244464082031e+01, 0.2111650433779e+01,
6789 0.6233108606023e-08, 0.4995232638403e+00, 0.4305306221819e+00,
6790 0.6877299149965e-08, 0.2834987233449e+01, 0.9561746721300e-02,
6791 0.8311234227190e-08, 0.2202951835758e+01, 0.3801276407308e+00,
6792 0.6599472832414e-08, 0.4478581462618e+01, 0.1063314406849e+01,
6793 0.6160491096549e-08, 0.5145858696411e+01, 0.1368660381889e+01,
6794 0.6164772043891e-08, 0.3762976697911e+00, 0.4234171675140e+00,
6795 0.6363248684450e-08, 0.3162246718685e+01, 0.1253008786510e-01,
6796 0.6448587520999e-08, 0.3442693302119e+01, 0.5287268506303e+00,
6797
6798 0.6431662283977e-08, 0.8977549136606e+00, 0.5306550935933e+00,
6799 0.6351223158474e-08, 0.4306447410369e+01, 0.5217580628120e+02,
6800 0.5476721393451e-08, 0.3888529177855e+01, 0.2221856701002e+01,
6801 0.5341772572619e-08, 0.2655560662512e+01, 0.7466759693650e-01,
6802 0.5337055758302e-08, 0.5164990735946e+01, 0.7489573444450e-01,
6803 0.5373120816787e-08, 0.6041214553456e+01, 0.1274714967946e+00,
6804 0.5392351705426e-08, 0.9177763485932e+00, 0.1055449481598e+01,
6805 0.6688495850205e-08, 0.3089608126937e+01, 0.2213766559277e+00,
6806 0.5072003660362e-08, 0.4311316541553e+01, 0.2132517061319e+00,
6807 0.5070726650455e-08, 0.5790675464444e+00, 0.2133464534247e+00,
6808
6809 0.5658012950032e-08, 0.2703945510675e+01, 0.7287631425543e+00,
6810 0.4835509924854e-08, 0.2975422976065e+01, 0.7160067364790e-01,
6811 0.6479821978012e-08, 0.1324168733114e+01, 0.2209183458640e-01,
6812 0.6230636494980e-08, 0.2860103632836e+01, 0.3306188016693e+00,
6813 0.4649239516213e-08, 0.4832259763403e+01, 0.7796265773310e-01,
6814 0.6487325792700e-08, 0.2726165825042e+01, 0.3884652414254e+00,
6815 0.4682823682770e-08, 0.6966602455408e+00, 0.1073608853559e+01,
6816 0.5704230804976e-08, 0.5669634104606e+01, 0.8731175355560e-01,
6817 0.6125413585489e-08, 0.1513386538915e+01, 0.7605151500000e-01,
6818 0.6035825038187e-08, 0.1983509168227e+01, 0.9846002785331e+00,
6819
6820 0.4331123462303e-08, 0.2782892992807e+01, 0.4297791515992e+00,
6821 0.4681107685143e-08, 0.5337232886836e+01, 0.2127790306879e+00,
6822 0.4669105829655e-08, 0.5837133792160e+01, 0.2138191288687e+00,
6823 0.5138823602365e-08, 0.3080560200507e+01, 0.7233337363710e-01,
6824 0.4615856664534e-08, 0.1661747897471e+01, 0.8603097737811e+00,
6825 0.4496916702197e-08, 0.2112508027068e+01, 0.7381754420900e-01,
6826 0.4278479042945e-08, 0.5716528462627e+01, 0.7574578717200e-01,
6827 0.3840525503932e-08, 0.6424172726492e+00, 0.3407705765729e+00,
6828 0.4866636509685e-08, 0.4919244697715e+01, 0.7722995774390e-01,
6829 0.3526100639296e-08, 0.2550821052734e+01, 0.6225157782540e-01,
6830
6831 0.3939558488075e-08, 0.3939331491710e+01, 0.5268983110410e-01,
6832 0.4041268772576e-08, 0.2275337571218e+01, 0.3503323232942e+00,
6833 0.3948761842853e-08, 0.1999324200790e+01, 0.1451108196653e+00,
6834 0.3258394550029e-08, 0.9121001378200e+00, 0.5296435984654e+00,
6835 0.3257897048761e-08, 0.3428428660869e+01, 0.5297383457582e+00,
6836 0.3842559031298e-08, 0.6132927720035e+01, 0.9098186128426e+00,
6837 0.3109920095448e-08, 0.7693650193003e+00, 0.3932462625300e-02,
6838 0.3132237775119e-08, 0.3621293854908e+01, 0.2346394437820e+00,
6839 0.3942189421510e-08, 0.4841863659733e+01, 0.3180992042600e-02,
6840 0.3796972285340e-08, 0.1814174994268e+01, 0.1862120789403e+00,
6841
6842 0.3995640233688e-08, 0.1386990406091e+01, 0.4549093064213e+00,
6843 0.2875013727414e-08, 0.9178318587177e+00, 0.1905464808669e+01,
6844 0.3073719932844e-08, 0.2688923811835e+01, 0.3628624111593e+00,
6845 0.2731016580075e-08, 0.1188259127584e+01, 0.2131850110243e+00,
6846 0.2729549896546e-08, 0.3702160634273e+01, 0.2134131485323e+00,
6847 0.3339372892449e-08, 0.7199163960331e+00, 0.2007689919132e+00,
6848 0.2898833764204e-08, 0.1916709364999e+01, 0.5291709230214e+00,
6849 0.2894536549362e-08, 0.2424043195547e+01, 0.5302110212022e+00,
6850 0.3096872473843e-08, 0.4445894977497e+01, 0.2976424921901e+00,
6851 0.2635672326810e-08, 0.3814366984117e+01, 0.1485980103780e+01,
6852
6853 0.3649302697001e-08, 0.2924200596084e+01, 0.6044726378023e+00,
6854 0.3127954585895e-08, 0.1842251648327e+01, 0.1084620721060e+00,
6855 0.2616040173947e-08, 0.4155841921984e+01, 0.1258454114666e+01,
6856 0.2597395859860e-08, 0.1158045978874e+00, 0.2103781122809e+00,
6857 0.2593286172210e-08, 0.4771850408691e+01, 0.2162200472757e+00,
6858 0.2481823585747e-08, 0.4608842558889e+00, 0.1062562936266e+01,
6859 0.2742219550725e-08, 0.1538781127028e+01, 0.5651155736444e+00,
6860 0.3199558469610e-08, 0.3226647822878e+00, 0.7036329877322e+00,
6861 0.2666088542957e-08, 0.1967991731219e+00, 0.1400015846597e+00,
6862 0.2397067430580e-08, 0.3707036669873e+01, 0.2125476091956e+00,
6863
6864 0.2376570772738e-08, 0.1182086628042e+01, 0.2140505503610e+00,
6865 0.2547228007887e-08, 0.4906256820629e+01, 0.1534957940063e+00,
6866 0.2265575594114e-08, 0.3414949866857e+01, 0.2235935264888e+00,
6867 0.2464381430585e-08, 0.4599122275378e+01, 0.2091065926078e+00,
6868 0.2433408527044e-08, 0.2830751145445e+00, 0.2174915669488e+00,
6869 0.2443605509076e-08, 0.4212046432538e+01, 0.1739420156204e+00,
6870 0.2319779262465e-08, 0.9881978408630e+00, 0.7530171478090e-01,
6871 0.2284622835465e-08, 0.5565347331588e+00, 0.7426161660010e-01,
6872 0.2467268750783e-08, 0.5655708150766e+00, 0.2526561439362e+00,
6873 0.2808513492782e-08, 0.1418405053408e+01, 0.5636314030725e+00,
6874
6875 0.2329528932532e-08, 0.4069557545675e+01, 0.1056200952181e+01,
6876 0.9698639532817e-09, 0.1074134313634e+01, 0.7826370942180e+02 };
6877
6878 /* SSB-to-Sun, T^0, Y */
6879 static final double s0y[] = {
6880 0.4955392320126e-02, 0.2170467313679e+01, 0.5296909721118e+00,
6881 0.2722325167392e-02, 0.2444433682196e+01, 0.2132990797783e+00,
6882 0.1546579925346e-02, 0.5992779281546e+00, 0.3813291813120e-01,
6883 0.8363140252966e-03, 0.7687356310801e+00, 0.7478166569050e-01,
6884 0.3385792683603e-03, 0.0000000000000e+00, 0.0000000000000e+00,
6885 0.1201192221613e-03, 0.2520035601514e+01, 0.1059381944224e+01,
6886 0.7587125720554e-04, 0.1669954006449e+01, 0.4265981595566e+00,
6887 0.1964155361250e-04, 0.5707743963343e+01, 0.2061856251104e+00,
6888 0.1891900364909e-04, 0.2320960679937e+01, 0.2204125344462e+00,
6889 0.1937373433356e-04, 0.3226940689555e+01, 0.1495633313810e+00,
6890
6891 0.1437139941351e-04, 0.2301626908096e+01, 0.5225775174439e+00,
6892 0.1406267683099e-04, 0.5188579265542e+01, 0.5368044267797e+00,
6893 0.1178703080346e-04, 0.5489483248476e+01, 0.7626583626240e-01,
6894 0.8079835186041e-05, 0.1683751835264e+01, 0.3664874755930e-01,
6895 0.7623253594652e-05, 0.2656400462961e+01, 0.3961708870310e-01,
6896 0.6248667483971e-05, 0.4992775362055e+01, 0.7329749511860e-01,
6897 0.4366353695038e-05, 0.2869706279678e+01, 0.1589072916335e+01,
6898 0.3829101568895e-05, 0.3572131359950e+01, 0.7113454667900e-02,
6899 0.3175733773908e-05, 0.4535372530045e+01, 0.4194847048887e+00,
6900 0.3092437902159e-05, 0.9230153317909e+00, 0.6398972393349e+00,
6901
6902 0.2874168812154e-05, 0.3363143761101e+01, 0.1102062672231e+00,
6903 0.3040119321826e-05, 0.3324250895675e+01, 0.6283075850446e+01,
6904 0.2699723308006e-05, 0.2917882441928e+00, 0.1030928125552e+00,
6905 0.2134832683534e-05, 0.4220997202487e+01, 0.3163918923335e+00,
6906 0.1770412139433e-05, 0.4747318496462e+01, 0.1021328554739e+02,
6907 0.1377264209373e-05, 0.4305058462401e+00, 0.1484170571900e-02,
6908 0.1127814538960e-05, 0.8538177240740e+00, 0.6327837846670e+00,
6909 0.1055608090130e-05, 0.1551800742580e+01, 0.4337116142245e+00,
6910 0.9802673861420e-06, 0.1459646735377e+01, 0.1052268489556e+01,
6911 0.1090329461951e-05, 0.1587351228711e+01, 0.1162474756779e+01,
6912
6913 0.6959590025090e-06, 0.5534442628766e+01, 0.1066495398892e+01,
6914 0.5664914529542e-06, 0.6030673003297e+01, 0.9491756770005e+00,
6915 0.6607787763599e-06, 0.4989507233927e+01, 0.8460828644453e+00,
6916 0.6269725742838e-06, 0.4222951804572e+01, 0.1480791608091e+00,
6917 0.6301889697863e-06, 0.5444316669126e+01, 0.2243449970715e+00,
6918 0.4891042662861e-06, 0.1490552839784e+01, 0.3340612434717e+01,
6919 0.3457083123290e-06, 0.3030475486049e+01, 0.3516457698740e-01,
6920 0.3032559967314e-06, 0.2652038793632e+01, 0.1104591729320e-01,
6921 0.2841133988903e-06, 0.1276744786829e+01, 0.4110125927500e-01,
6922 0.2855564444432e-06, 0.2143368674733e+01, 0.1510475019529e+00,
6923
6924 0.2765157135038e-06, 0.5444186109077e+01, 0.6373574839730e-01,
6925 0.2382312465034e-06, 0.2190521137593e+01, 0.2275259891141e+00,
6926 0.2808060365077e-06, 0.5735195064841e+01, 0.2535050500000e-01,
6927 0.2332175234405e-06, 0.9481985524859e-01, 0.7181332454670e-01,
6928 0.2322488199659e-06, 0.5180499361533e+01, 0.8582758298370e-01,
6929 0.1881850258423e-06, 0.3219788273885e+01, 0.2118763888447e+01,
6930 0.2196111392808e-06, 0.2366941159761e+01, 0.2968341143800e-02,
6931 0.2183810335519e-06, 0.4825445110915e+01, 0.7775000683430e-01,
6932 0.2002733093326e-06, 0.2457148995307e+01, 0.2093666171530e+00,
6933 0.1967111767229e-06, 0.5586291545459e+01, 0.2172315424036e+00,
6934
6935 0.1568473250543e-06, 0.3708003123320e+01, 0.7429900518901e+00,
6936 0.1852528314300e-06, 0.4310638151560e+01, 0.2022531624851e+00,
6937 0.1832111226447e-06, 0.1494665322656e+01, 0.3235053470014e+00,
6938 0.1746805502310e-06, 0.1451378500784e+01, 0.1385174140878e+00,
6939 0.1555730966650e-06, 0.1068040418198e+01, 0.7358765972222e+00,
6940 0.1554883462559e-06, 0.2442579035461e+01, 0.5154640627760e+00,
6941 0.1638380568746e-06, 0.2597913420625e+00, 0.8531963191132e+00,
6942 0.1159938593640e-06, 0.5834512021280e+01, 0.1990721704425e+00,
6943 0.1083427965695e-06, 0.5054033177950e+01, 0.5439178814476e+00,
6944 0.1156480369431e-06, 0.5325677432457e+01, 0.5257585094865e+00,
6945
6946 0.1141308860095e-06, 0.2153403923857e+01, 0.5336234347371e+00,
6947 0.7913146470946e-07, 0.8642846847027e+00, 0.1478866649112e+01,
6948 0.7439752463733e-07, 0.1970628496213e+01, 0.2164800718209e+00,
6949 0.7280277104079e-07, 0.6073307250609e+01, 0.2101180877357e+00,
6950 0.8319567719136e-07, 0.1954371928334e+01, 0.1692165728891e+01,
6951 0.7137705549290e-07, 0.8904989440909e+00, 0.4155522422634e+00,
6952 0.6900825396225e-07, 0.2825717714977e+01, 0.1173197218910e+00,
6953 0.7245757216635e-07, 0.2481677513331e+01, 0.1265567569334e+01,
6954 0.6961165696255e-07, 0.1292955312978e+01, 0.9562891316684e+00,
6955 0.7571804456890e-07, 0.3427517575069e+01, 0.1422690933580e-01,
6956
6957 0.6605425721904e-07, 0.8052192701492e+00, 0.6470106940028e+00,
6958 0.7375477357248e-07, 0.1705076390088e+01, 0.1581959461667e+01,
6959 0.7041664951470e-07, 0.4848356967891e+00, 0.9597935788730e-01,
6960 0.6322199535763e-07, 0.3878069473909e+01, 0.7084920306520e-01,
6961 0.5244380279191e-07, 0.2645560544125e+01, 0.5265099800692e+00,
6962 0.5143125704988e-07, 0.4834486101370e+01, 0.5328719641544e+00,
6963 0.5871866319373e-07, 0.7981472548900e+00, 0.7871412831580e-01,
6964 0.6300822573871e-07, 0.5979398788281e+01, 0.2608790314060e+02,
6965 0.6062154271548e-07, 0.4108655402756e+01, 0.1114304132498e+00,
6966 0.4361912339976e-07, 0.5322624319280e+01, 0.1375773836557e+01,
6967
6968 0.4417005920067e-07, 0.6240817359284e+01, 0.2770348281756e+00,
6969 0.4686806749936e-07, 0.3214977301156e+01, 0.1143987543936e+00,
6970 0.3758892132305e-07, 0.5879809634765e+01, 0.1596186371003e+01,
6971 0.5151351332319e-07, 0.2893377688007e+00, 0.2228608264996e+00,
6972 0.4554683578572e-07, 0.5475427144122e+01, 0.1465949902372e+00,
6973 0.3442381385338e-07, 0.5992034796640e+01, 0.5070101000000e-01,
6974 0.2831093954933e-07, 0.5367350273914e+01, 0.3092784376656e+00,
6975 0.3756267090084e-07, 0.5758171285420e+01, 0.4903339079539e+00,
6976 0.2816374679892e-07, 0.1863718700923e+01, 0.2991266627620e+00,
6977 0.3419307025569e-07, 0.9524347534130e+00, 0.3518164938661e+00,
6978
6979 0.2904250494239e-07, 0.5304471615602e+01, 0.1099462426779e+00,
6980 0.2471734511206e-07, 0.1297069793530e+01, 0.6256703299991e+00,
6981 0.2539620831872e-07, 0.3281126083375e+01, 0.1256615170089e+02,
6982 0.2281017868007e-07, 0.1829122133165e+01, 0.6681224869435e+01,
6983 0.2275319473335e-07, 0.5797198160181e+01, 0.3932462625300e-02,
6984 0.2547755368442e-07, 0.4752697708330e+01, 0.1169588211447e+01,
6985 0.2285979669317e-07, 0.1223205292886e+01, 0.1045155034888e+01,
6986 0.1913386560994e-07, 0.1757532993389e+01, 0.1155361302111e+01,
6987 0.1809020525147e-07, 0.4246116108791e+01, 0.3368040641550e-01,
6988 0.1649213300201e-07, 0.1445162890627e+01, 0.4408250688924e+00,
6989
6990 0.1834972793932e-07, 0.1126917567225e+01, 0.4452511715700e-02,
6991 0.1439550648138e-07, 0.6160756834764e+01, 0.9420622223326e+00,
6992 0.1487645457041e-07, 0.4358761931792e+01, 0.4123712502208e+00,
6993 0.1731729516660e-07, 0.6134456753344e+01, 0.2108507877249e+00,
6994 0.1717747163567e-07, 0.1898186084455e+01, 0.2157473718317e+00,
6995 0.1418190430374e-07, 0.4180286741266e+01, 0.6521991896920e-01,
6996 0.1404844134873e-07, 0.7654053565412e-01, 0.4258542984690e-01,
6997 0.1409842846538e-07, 0.4418612420312e+01, 0.2258291676434e+00,
6998 0.1090948346291e-07, 0.1260615686131e+01, 0.4226656969313e+00,
6999 0.1357577323612e-07, 0.3558248818690e+01, 0.7923417740620e-01,
7000
7001 0.1018154061960e-07, 0.5676087241256e+01, 0.1456308687557e+00,
7002 0.1412073972109e-07, 0.8394392632422e+00, 0.1525316725248e+00,
7003 0.1030938326496e-07, 0.1653593274064e+01, 0.1795258541446e+01,
7004 0.1180081567104e-07, 0.1285802592036e+01, 0.7032915397480e-01,
7005 0.9708510575650e-08, 0.7631889488106e+00, 0.8434341241180e-01,
7006 0.9637689663447e-08, 0.4630642649176e+01, 0.1272681024002e+01,
7007 0.1068910429389e-07, 0.5294934032165e+01, 0.2123349582968e+00,
7008 0.1063716179336e-07, 0.2736266800832e+01, 0.2142632012598e+00,
7009 0.1234858713814e-07, 0.1302891146570e+01, 0.1847279083684e+00,
7010 0.8912631189738e-08, 0.3570415993621e+01, 0.2648454860559e+01,
7011
7012 0.1036378285534e-07, 0.4236693440949e+01, 0.1370332435159e+00,
7013 0.9667798501561e-08, 0.2960768892398e+01, 0.4376440768498e+00,
7014 0.8108314201902e-08, 0.6987781646841e+00, 0.2880807454688e+00,
7015 0.7648364324628e-08, 0.2499017863863e+01, 0.2037373330570e+00,
7016 0.7286136828406e-08, 0.3787426951665e+01, 0.1129145838217e+00,
7017 0.9448237743913e-08, 0.2694354332983e+01, 0.5272426800584e+00,
7018 0.9374276106428e-08, 0.4787121277064e+01, 0.5321392641652e+00,
7019 0.7100226287462e-08, 0.3530238792101e+00, 0.6288513220417e+00,
7020 0.9253056659571e-08, 0.1399478925664e+01, 0.1606092486742e+00,
7021 0.6636432145504e-08, 0.3479575438447e+01, 0.1368660381889e+01,
7022
7023 0.6469975312932e-08, 0.1383669964800e+01, 0.2008557621224e+01,
7024 0.7335849729765e-08, 0.1243698166898e+01, 0.9561746721300e-02,
7025 0.8743421205855e-08, 0.3776164289301e+01, 0.3801276407308e+00,
7026 0.5993635744494e-08, 0.5627122113596e+01, 0.2042657109477e+02,
7027 0.5981008479693e-08, 0.1674336636752e+01, 0.2111650433779e+01,
7028 0.6188535145838e-08, 0.5214925208672e+01, 0.4305306221819e+00,
7029 0.6596074017566e-08, 0.2907653268124e+01, 0.1063314406849e+01,
7030 0.6630815126226e-08, 0.2127643669658e+01, 0.8389694097774e+00,
7031 0.6156772830040e-08, 0.5082160803295e+01, 0.4234171675140e+00,
7032 0.6446960563014e-08, 0.1872100916905e+01, 0.5287268506303e+00,
7033
7034 0.6429324424668e-08, 0.5610276103577e+01, 0.5306550935933e+00,
7035 0.6302232396465e-08, 0.1592152049607e+01, 0.1253008786510e-01,
7036 0.6399244436159e-08, 0.2746214421532e+01, 0.5217580628120e+02,
7037 0.5474965172558e-08, 0.2317666374383e+01, 0.2221856701002e+01,
7038 0.5339293190692e-08, 0.1084724961156e+01, 0.7466759693650e-01,
7039 0.5334733683389e-08, 0.3594106067745e+01, 0.7489573444450e-01,
7040 0.5392665782110e-08, 0.5630254365606e+01, 0.1055449481598e+01,
7041 0.6682075673789e-08, 0.1518480041732e+01, 0.2213766559277e+00,
7042 0.5079130495960e-08, 0.2739765115711e+01, 0.2132517061319e+00,
7043 0.5077759793261e-08, 0.5290711290094e+01, 0.2133464534247e+00,
7044
7045 0.4832037368310e-08, 0.1404473217200e+01, 0.7160067364790e-01,
7046 0.6463279674802e-08, 0.6038381695210e+01, 0.2209183458640e-01,
7047 0.6240592771560e-08, 0.1290170653666e+01, 0.3306188016693e+00,
7048 0.4672013521493e-08, 0.3261895939677e+01, 0.7796265773310e-01,
7049 0.6500650750348e-08, 0.1154522312095e+01, 0.3884652414254e+00,
7050 0.6344161389053e-08, 0.6206111545062e+01, 0.7605151500000e-01,
7051 0.4682518370646e-08, 0.5409118796685e+01, 0.1073608853559e+01,
7052 0.5329460015591e-08, 0.1202985784864e+01, 0.7287631425543e+00,
7053 0.5701588675898e-08, 0.4098715257064e+01, 0.8731175355560e-01,
7054 0.6030690867211e-08, 0.4132033218460e+00, 0.9846002785331e+00,
7055
7056 0.4336256312655e-08, 0.1211415991827e+01, 0.4297791515992e+00,
7057 0.4688498808975e-08, 0.3765479072409e+01, 0.2127790306879e+00,
7058 0.4675578609335e-08, 0.4265540037226e+01, 0.2138191288687e+00,
7059 0.4225578112158e-08, 0.5237566010676e+01, 0.3407705765729e+00,
7060 0.5139422230028e-08, 0.1507173079513e+01, 0.7233337363710e-01,
7061 0.4619995093571e-08, 0.9023957449848e-01, 0.8603097737811e+00,
7062 0.4494776255461e-08, 0.5414930552139e+00, 0.7381754420900e-01,
7063 0.4274026276788e-08, 0.4145735303659e+01, 0.7574578717200e-01,
7064 0.5018141789353e-08, 0.3344408829055e+01, 0.3180992042600e-02,
7065 0.4866163952181e-08, 0.3348534657607e+01, 0.7722995774390e-01,
7066
7067 0.4111986020501e-08, 0.4198823597220e+00, 0.1451108196653e+00,
7068 0.3356142784950e-08, 0.5609144747180e+01, 0.1274714967946e+00,
7069 0.4070575554551e-08, 0.7028411059224e+00, 0.3503323232942e+00,
7070 0.3257451857278e-08, 0.5624697983086e+01, 0.5296435984654e+00,
7071 0.3256973703026e-08, 0.1857842076707e+01, 0.5297383457582e+00,
7072 0.3830771508640e-08, 0.4562887279931e+01, 0.9098186128426e+00,
7073 0.3725024005962e-08, 0.2358058692652e+00, 0.1084620721060e+00,
7074 0.3136763921756e-08, 0.2049731526845e+01, 0.2346394437820e+00,
7075 0.3795147256194e-08, 0.2432356296933e+00, 0.1862120789403e+00,
7076 0.2877342229911e-08, 0.5631101279387e+01, 0.1905464808669e+01,
7077
7078 0.3076931798805e-08, 0.1117615737392e+01, 0.3628624111593e+00,
7079 0.2734765945273e-08, 0.5899826516955e+01, 0.2131850110243e+00,
7080 0.2733405296885e-08, 0.2130562964070e+01, 0.2134131485323e+00,
7081 0.2898552353410e-08, 0.3462387048225e+00, 0.5291709230214e+00,
7082 0.2893736103681e-08, 0.8534352781543e+00, 0.5302110212022e+00,
7083 0.3095717734137e-08, 0.2875061429041e+01, 0.2976424921901e+00,
7084 0.2636190425832e-08, 0.2242512846659e+01, 0.1485980103780e+01,
7085 0.3645512095537e-08, 0.1354016903958e+01, 0.6044726378023e+00,
7086 0.2808173547723e-08, 0.6705114365631e-01, 0.6225157782540e-01,
7087 0.2625012866888e-08, 0.4775705748482e+01, 0.5268983110410e-01,
7088
7089 0.2572233995651e-08, 0.2638924216139e+01, 0.1258454114666e+01,
7090 0.2604238824792e-08, 0.4826358927373e+01, 0.2103781122809e+00,
7091 0.2596886385239e-08, 0.3200388483118e+01, 0.2162200472757e+00,
7092 0.3228057304264e-08, 0.5384848409563e+01, 0.2007689919132e+00,
7093 0.2481601798252e-08, 0.5173373487744e+01, 0.1062562936266e+01,
7094 0.2745977498864e-08, 0.6250966149853e+01, 0.5651155736444e+00,
7095 0.2669878833811e-08, 0.4906001352499e+01, 0.1400015846597e+00,
7096 0.3203986611711e-08, 0.5034333010005e+01, 0.7036329877322e+00,
7097 0.3354961227212e-08, 0.6108262423137e+01, 0.4549093064213e+00,
7098 0.2400407324558e-08, 0.2135399294955e+01, 0.2125476091956e+00,
7099
7100 0.2379905859802e-08, 0.5893721933961e+01, 0.2140505503610e+00,
7101 0.2550844302187e-08, 0.3331940762063e+01, 0.1534957940063e+00,
7102 0.2268824211001e-08, 0.1843418461035e+01, 0.2235935264888e+00,
7103 0.2464700891204e-08, 0.3029548547230e+01, 0.2091065926078e+00,
7104 0.2436814726024e-08, 0.4994717970364e+01, 0.2174915669488e+00,
7105 0.2443623894745e-08, 0.2645102591375e+01, 0.1739420156204e+00,
7106 0.2318701783838e-08, 0.5700547397897e+01, 0.7530171478090e-01,
7107 0.2284448700256e-08, 0.5268898905872e+01, 0.7426161660010e-01,
7108 0.2468848123510e-08, 0.5276280575078e+01, 0.2526561439362e+00,
7109 0.2814052350303e-08, 0.6130168623475e+01, 0.5636314030725e+00,
7110
7111 0.2243662755220e-08, 0.6631692457995e+00, 0.8886590321940e-01,
7112 0.2330795855941e-08, 0.2499435487702e+01, 0.1056200952181e+01,
7113 0.9757679038404e-09, 0.5796846023126e+01, 0.7826370942180e+02 };
7114
7115 /* SSB-to-Sun, T^0, Z */
7116 static final double s0z[] = {
7117 0.1181255122986e-03, 0.4607918989164e+00, 0.2132990797783e+00,
7118 0.1127777651095e-03, 0.4169146331296e+00, 0.5296909721118e+00,
7119 0.4777754401806e-04, 0.4582657007130e+01, 0.3813291813120e-01,
7120 0.1129354285772e-04, 0.5758735142480e+01, 0.7478166569050e-01,
7121 -0.1149543637123e-04, 0.0000000000000e+00, 0.0000000000000e+00,
7122 0.3298730512306e-05, 0.5978801994625e+01, 0.4265981595566e+00,
7123 0.2733376706079e-05, 0.7665413691040e+00, 0.1059381944224e+01,
7124 0.9426389657270e-06, 0.3710201265838e+01, 0.2061856251104e+00,
7125 0.8187517749552e-06, 0.3390675605802e+00, 0.2204125344462e+00,
7126 0.4080447871819e-06, 0.4552296640088e+00, 0.5225775174439e+00,
7127
7128 0.3169973017028e-06, 0.3445455899321e+01, 0.5368044267797e+00,
7129 0.2438098615549e-06, 0.5664675150648e+01, 0.3664874755930e-01,
7130 0.2601897517235e-06, 0.1931894095697e+01, 0.1495633313810e+00,
7131 0.2314558080079e-06, 0.3666319115574e+00, 0.3961708870310e-01,
7132 0.1962549548002e-06, 0.3167411699020e+01, 0.7626583626240e-01,
7133 0.2180518287925e-06, 0.1544420746580e+01, 0.7113454667900e-02,
7134 0.1451382442868e-06, 0.1583756740070e+01, 0.1102062672231e+00,
7135 0.1358439007389e-06, 0.5239941758280e+01, 0.6398972393349e+00,
7136 0.1050585898028e-06, 0.2266958352859e+01, 0.3163918923335e+00,
7137 0.1050029870186e-06, 0.2711495250354e+01, 0.4194847048887e+00,
7138
7139 0.9934920679800e-07, 0.1116208151396e+01, 0.1589072916335e+01,
7140 0.1048395331560e-06, 0.3408619600206e+01, 0.1021328554739e+02,
7141 0.8370147196668e-07, 0.3810459401087e+01, 0.2535050500000e-01,
7142 0.7989856510998e-07, 0.3769910473647e+01, 0.7329749511860e-01,
7143 0.5441221655233e-07, 0.2416994903374e+01, 0.1030928125552e+00,
7144 0.4610812906784e-07, 0.5858503336994e+01, 0.4337116142245e+00,
7145 0.3923022803444e-07, 0.3354170010125e+00, 0.1484170571900e-02,
7146 0.2610725582128e-07, 0.5410600646324e+01, 0.6327837846670e+00,
7147 0.2455279767721e-07, 0.6120216681403e+01, 0.1162474756779e+01,
7148 0.2375530706525e-07, 0.6055443426143e+01, 0.1052268489556e+01,
7149
7150 0.1782967577553e-07, 0.3146108708004e+01, 0.8460828644453e+00,
7151 0.1581687095238e-07, 0.6255496089819e+00, 0.3340612434717e+01,
7152 0.1594657672461e-07, 0.3782604300261e+01, 0.1066495398892e+01,
7153 0.1563448615040e-07, 0.1997775733196e+01, 0.2022531624851e+00,
7154 0.1463624258525e-07, 0.1736316792088e+00, 0.3516457698740e-01,
7155 0.1331585056673e-07, 0.4331941830747e+01, 0.9491756770005e+00,
7156 0.1130634557637e-07, 0.6152017751825e+01, 0.2968341143800e-02,
7157 0.1028949607145e-07, 0.2101792614637e+00, 0.2275259891141e+00,
7158 0.1024074971618e-07, 0.4071833211074e+01, 0.5070101000000e-01,
7159 0.8826956060303e-08, 0.4861633688145e+00, 0.2093666171530e+00,
7160
7161 0.8572230171541e-08, 0.5268190724302e+01, 0.4110125927500e-01,
7162 0.7649332643544e-08, 0.5134543417106e+01, 0.2608790314060e+02,
7163 0.8581673291033e-08, 0.2920218146681e+01, 0.1480791608091e+00,
7164 0.8430589300938e-08, 0.3604576619108e+01, 0.2172315424036e+00,
7165 0.7776165501012e-08, 0.3772942249792e+01, 0.6373574839730e-01,
7166 0.8311070234408e-08, 0.6200412329888e+01, 0.3235053470014e+00,
7167 0.6927365212582e-08, 0.4543353113437e+01, 0.8531963191132e+00,
7168 0.6791574208598e-08, 0.2882188406238e+01, 0.7181332454670e-01,
7169 0.5593100811839e-08, 0.1776646892780e+01, 0.7429900518901e+00,
7170 0.4553381853021e-08, 0.3949617611240e+01, 0.7775000683430e-01,
7171
7172 0.5758000450068e-08, 0.3859251775075e+01, 0.1990721704425e+00,
7173 0.4281283457133e-08, 0.1466294631206e+01, 0.2118763888447e+01,
7174 0.4206935661097e-08, 0.5421776011706e+01, 0.1104591729320e-01,
7175 0.4213751641837e-08, 0.3412048993322e+01, 0.2243449970715e+00,
7176 0.5310506239878e-08, 0.5421641370995e+00, 0.5154640627760e+00,
7177 0.3827450341320e-08, 0.8887314524995e+00, 0.1510475019529e+00,
7178 0.4292435241187e-08, 0.1405043757194e+01, 0.1422690933580e-01,
7179 0.3189780702289e-08, 0.1060049293445e+01, 0.1173197218910e+00,
7180 0.3226611928069e-08, 0.6270858897442e+01, 0.2164800718209e+00,
7181 0.2893897608830e-08, 0.5117563223301e+01, 0.6470106940028e+00,
7182
7183 0.3239852024578e-08, 0.4079092237983e+01, 0.2101180877357e+00,
7184 0.2956892222200e-08, 0.1594917021704e+01, 0.3092784376656e+00,
7185 0.2980177912437e-08, 0.5258787667564e+01, 0.4155522422634e+00,
7186 0.3163725690776e-08, 0.3854589225479e+01, 0.8582758298370e-01,
7187 0.2662262399118e-08, 0.3561326430187e+01, 0.5257585094865e+00,
7188 0.2766689135729e-08, 0.3180732086830e+00, 0.1385174140878e+00,
7189 0.2411600278464e-08, 0.3324798335058e+01, 0.5439178814476e+00,
7190 0.2483527695131e-08, 0.4169069291947e+00, 0.5336234347371e+00,
7191 0.7788777276590e-09, 0.1900569908215e+01, 0.5217580628120e+02 };
7192
7193 /* SSB-to-Sun, T^1, X */
7194 static final double s1x[] = {
7195 -0.1296310361520e-07, 0.0000000000000e+00, 0.0000000000000e+00,
7196 0.8975769009438e-08, 0.1128891609250e+01, 0.4265981595566e+00,
7197 0.7771113441307e-08, 0.2706039877077e+01, 0.2061856251104e+00,
7198 0.7538303866642e-08, 0.2191281289498e+01, 0.2204125344462e+00,
7199 0.6061384579336e-08, 0.3248167319958e+01, 0.1059381944224e+01,
7200 0.5726994235594e-08, 0.5569981398610e+01, 0.5225775174439e+00,
7201 0.5616492836424e-08, 0.5057386614909e+01, 0.5368044267797e+00,
7202 0.1010881584769e-08, 0.3473577116095e+01, 0.7113454667900e-02,
7203 0.7259606157626e-09, 0.3651858593665e+00, 0.6398972393349e+00,
7204 0.8755095026935e-09, 0.1662835408338e+01, 0.4194847048887e+00,
7205
7206 0.5370491182812e-09, 0.1327673878077e+01, 0.4337116142245e+00,
7207 0.5743773887665e-09, 0.4250200846687e+01, 0.2132990797783e+00,
7208 0.4408103140300e-09, 0.3598752574277e+01, 0.1589072916335e+01,
7209 0.3101892374445e-09, 0.4887822983319e+01, 0.1052268489556e+01,
7210 0.3209453713578e-09, 0.9702272295114e+00, 0.5296909721118e+00,
7211 0.3017228286064e-09, 0.5484462275949e+01, 0.1066495398892e+01,
7212 0.3200700038601e-09, 0.2846613338643e+01, 0.1495633313810e+00,
7213 0.2137637279911e-09, 0.5692163292729e+00, 0.3163918923335e+00,
7214 0.1899686386727e-09, 0.2061077157189e+01, 0.2275259891141e+00,
7215 0.1401994545308e-09, 0.4177771136967e+01, 0.1102062672231e+00,
7216
7217 0.1578057810499e-09, 0.5782460597335e+01, 0.7626583626240e-01,
7218 0.1237713253351e-09, 0.5705900866881e+01, 0.5154640627760e+00,
7219 0.1313076837395e-09, 0.5163438179576e+01, 0.3664874755930e-01,
7220 0.1184963304860e-09, 0.3054804427242e+01, 0.6327837846670e+00,
7221 0.1238130878565e-09, 0.2317292575962e+01, 0.3961708870310e-01,
7222 0.1015959527736e-09, 0.2194643645526e+01, 0.7329749511860e-01,
7223 0.9017954423714e-10, 0.2868603545435e+01, 0.1990721704425e+00,
7224 0.8668024955603e-10, 0.4923849675082e+01, 0.5439178814476e+00,
7225 0.7756083930103e-10, 0.3014334135200e+01, 0.9491756770005e+00,
7226 0.7536503401741e-10, 0.2704886279769e+01, 0.1030928125552e+00,
7227
7228 0.5483308679332e-10, 0.6010983673799e+01, 0.8531963191132e+00,
7229 0.5184339620428e-10, 0.1952704573291e+01, 0.2093666171530e+00,
7230 0.5108658712030e-10, 0.2958575786649e+01, 0.2172315424036e+00,
7231 0.5019424524650e-10, 0.1736317621318e+01, 0.2164800718209e+00,
7232 0.4909312625978e-10, 0.3167216416257e+01, 0.2101180877357e+00,
7233 0.4456638901107e-10, 0.7697579923471e+00, 0.3235053470014e+00,
7234 0.4227030350925e-10, 0.3490910137928e+01, 0.6373574839730e-01,
7235 0.4095456040093e-10, 0.5178888984491e+00, 0.6470106940028e+00,
7236 0.4990537041422e-10, 0.3323887668974e+01, 0.1422690933580e-01,
7237 0.4321170010845e-10, 0.4288484987118e+01, 0.7358765972222e+00,
7238
7239 0.3544072091802e-10, 0.6021051579251e+01, 0.5265099800692e+00,
7240 0.3480198638687e-10, 0.4600027054714e+01, 0.5328719641544e+00,
7241 0.3440287244435e-10, 0.4349525970742e+01, 0.8582758298370e-01,
7242 0.3330628322713e-10, 0.2347391505082e+01, 0.1104591729320e-01,
7243 0.2973060707184e-10, 0.4789409286400e+01, 0.5257585094865e+00,
7244 0.2932606766089e-10, 0.5831693799927e+01, 0.5336234347371e+00,
7245 0.2876972310953e-10, 0.2692638514771e+01, 0.1173197218910e+00,
7246 0.2827488278556e-10, 0.2056052487960e+01, 0.2022531624851e+00,
7247 0.2515028239756e-10, 0.7411863262449e+00, 0.9597935788730e-01,
7248 0.2853033744415e-10, 0.3948481024894e+01, 0.2118763888447e+01 };
7249
7250 /* SSB-to-Sun, T^1, Y */
7251 static final double s1y[] = {
7252 0.8989047573576e-08, 0.5840593672122e+01, 0.4265981595566e+00,
7253 0.7815938401048e-08, 0.1129664707133e+01, 0.2061856251104e+00,
7254 0.7550926713280e-08, 0.6196589104845e+00, 0.2204125344462e+00,
7255 0.6056556925895e-08, 0.1677494667846e+01, 0.1059381944224e+01,
7256 0.5734142698204e-08, 0.4000920852962e+01, 0.5225775174439e+00,
7257 0.5614341822459e-08, 0.3486722577328e+01, 0.5368044267797e+00,
7258 0.1028678147656e-08, 0.1877141024787e+01, 0.7113454667900e-02,
7259 0.7270792075266e-09, 0.5077167301739e+01, 0.6398972393349e+00,
7260 0.8734141726040e-09, 0.9069550282609e-01, 0.4194847048887e+00,
7261 0.5377371402113e-09, 0.6039381844671e+01, 0.4337116142245e+00,
7262
7263 0.4729719431571e-09, 0.2153086311760e+01, 0.2132990797783e+00,
7264 0.4458052820973e-09, 0.5059830025565e+01, 0.5296909721118e+00,
7265 0.4406855467908e-09, 0.2027971692630e+01, 0.1589072916335e+01,
7266 0.3101659310977e-09, 0.3317677981860e+01, 0.1052268489556e+01,
7267 0.3016749232545e-09, 0.3913703482532e+01, 0.1066495398892e+01,
7268 0.3198541352656e-09, 0.1275513098525e+01, 0.1495633313810e+00,
7269 0.2142065389871e-09, 0.5301351614597e+01, 0.3163918923335e+00,
7270 0.1902615247592e-09, 0.4894943352736e+00, 0.2275259891141e+00,
7271 0.1613410990871e-09, 0.2449891130437e+01, 0.1102062672231e+00,
7272 0.1576992165097e-09, 0.4211421447633e+01, 0.7626583626240e-01,
7273
7274 0.1241637259894e-09, 0.4140803368133e+01, 0.5154640627760e+00,
7275 0.1313974830355e-09, 0.3591920305503e+01, 0.3664874755930e-01,
7276 0.1181697118258e-09, 0.1506314382788e+01, 0.6327837846670e+00,
7277 0.1238239742779e-09, 0.7461405378404e+00, 0.3961708870310e-01,
7278 0.1010107068241e-09, 0.6271010795475e+00, 0.7329749511860e-01,
7279 0.9226316616509e-10, 0.1259158839583e+01, 0.1990721704425e+00,
7280 0.8664946419555e-10, 0.3353244696934e+01, 0.5439178814476e+00,
7281 0.7757230468978e-10, 0.1447677295196e+01, 0.9491756770005e+00,
7282 0.7693168628139e-10, 0.1120509896721e+01, 0.1030928125552e+00,
7283 0.5487897454612e-10, 0.4439380426795e+01, 0.8531963191132e+00,
7284
7285 0.5196118677218e-10, 0.3788856619137e+00, 0.2093666171530e+00,
7286 0.5110853339935e-10, 0.1386879372016e+01, 0.2172315424036e+00,
7287 0.5027804534813e-10, 0.1647881805466e+00, 0.2164800718209e+00,
7288 0.4922485922674e-10, 0.1594315079862e+01, 0.2101180877357e+00,
7289 0.6155599524400e-10, 0.0000000000000e+00, 0.0000000000000e+00,
7290 0.4447147832161e-10, 0.5480720918976e+01, 0.3235053470014e+00,
7291 0.4144691276422e-10, 0.1931371033660e+01, 0.6373574839730e-01,
7292 0.4099950625452e-10, 0.5229611294335e+01, 0.6470106940028e+00,
7293 0.5060541682953e-10, 0.1731112486298e+01, 0.1422690933580e-01,
7294 0.4293615946300e-10, 0.2714571038925e+01, 0.7358765972222e+00,
7295
7296 0.3545659845763e-10, 0.4451041444634e+01, 0.5265099800692e+00,
7297 0.3479112041196e-10, 0.3029385448081e+01, 0.5328719641544e+00,
7298 0.3438516493570e-10, 0.2778507143731e+01, 0.8582758298370e-01,
7299 0.3297341285033e-10, 0.7898709807584e+00, 0.1104591729320e-01,
7300 0.2972585818015e-10, 0.3218785316973e+01, 0.5257585094865e+00,
7301 0.2931707295017e-10, 0.4260731012098e+01, 0.5336234347371e+00,
7302 0.2897198149403e-10, 0.1120753978101e+01, 0.1173197218910e+00,
7303 0.2832293240878e-10, 0.4597682717827e+00, 0.2022531624851e+00,
7304 0.2864348326612e-10, 0.2169939928448e+01, 0.9597935788730e-01,
7305 0.2852714675471e-10, 0.2377659870578e+01, 0.2118763888447e+01 };
7306
7307 /* SSB-to-Sun, T^1, Z */
7308 static final double s1z[] = {
7309 0.5444220475678e-08, 0.1803825509310e+01, 0.2132990797783e+00,
7310 0.3883412695596e-08, 0.4668616389392e+01, 0.5296909721118e+00,
7311 0.1334341434551e-08, 0.0000000000000e+00, 0.0000000000000e+00,
7312 0.3730001266883e-09, 0.5401405918943e+01, 0.2061856251104e+00,
7313 0.2894929197956e-09, 0.4932415609852e+01, 0.2204125344462e+00,
7314 0.2857950357701e-09, 0.3154625362131e+01, 0.7478166569050e-01,
7315 0.2499226432292e-09, 0.3657486128988e+01, 0.4265981595566e+00,
7316 0.1937705443593e-09, 0.5740434679002e+01, 0.1059381944224e+01,
7317 0.1374894396320e-09, 0.1712857366891e+01, 0.5368044267797e+00,
7318 0.1217248678408e-09, 0.2312090870932e+01, 0.5225775174439e+00,
7319
7320 0.7961052740870e-10, 0.5283368554163e+01, 0.3813291813120e-01,
7321 0.4979225949689e-10, 0.4298290471860e+01, 0.4194847048887e+00,
7322 0.4388552286597e-10, 0.6145515047406e+01, 0.7113454667900e-02,
7323 0.2586835212560e-10, 0.3019448001809e+01, 0.6398972393349e+00 };
7324
7325 /* SSB-to-Sun, T^2, X */
7326 static final double s2x[] = {
7327 0.1603551636587e-11, 0.4404109410481e+01, 0.2061856251104e+00,
7328 0.1556935889384e-11, 0.4818040873603e+00, 0.2204125344462e+00,
7329 0.1182594414915e-11, 0.9935762734472e+00, 0.5225775174439e+00,
7330 0.1158794583180e-11, 0.3353180966450e+01, 0.5368044267797e+00,
7331 0.9597358943932e-12, 0.5567045358298e+01, 0.2132990797783e+00,
7332 0.6511516579605e-12, 0.5630872420788e+01, 0.4265981595566e+00,
7333 0.7419792747688e-12, 0.2156188581957e+01, 0.5296909721118e+00,
7334 0.3951972655848e-12, 0.1981022541805e+01, 0.1059381944224e+01,
7335 0.4478223877045e-12, 0.0000000000000e+00, 0.0000000000000e+00 };
7336
7337 /* SSB-to-Sun, T^2, Y */
7338 static final double s2y[] = {
7339 0.1609114495091e-11, 0.2831096993481e+01, 0.2061856251104e+00,
7340 0.1560330784946e-11, 0.5193058213906e+01, 0.2204125344462e+00,
7341 0.1183535479202e-11, 0.5707003443890e+01, 0.5225775174439e+00,
7342 0.1158183066182e-11, 0.1782400404928e+01, 0.5368044267797e+00,
7343 0.1032868027407e-11, 0.4036925452011e+01, 0.2132990797783e+00,
7344 0.6540142847741e-12, 0.4058241056717e+01, 0.4265981595566e+00,
7345 0.7305236491596e-12, 0.6175401942957e+00, 0.5296909721118e+00,
7346 -0.5580725052968e-12, 0.0000000000000e+00, 0.0000000000000e+00,
7347 0.3946122651015e-12, 0.4108265279171e+00, 0.1059381944224e+01 };
7348
7349 /* SSB-to-Sun, T^2, Z */
7350 static final double s2z[] = {
7351 0.3749920358054e-12, 0.3230285558668e+01, 0.2132990797783e+00,
7352 0.2735037220939e-12, 0.6154322683046e+01, 0.5296909721118e+00 };
7353 }
7354
7355 /**
7356 * Earth position and velocity, heliocentric and barycentric, with
7357 * respect to the Barycentric Celestial Reference System.
7358 *
7359 *<p>This function is derived from the International Astronomical Union's
7360 * SOFA (Standards Of Fundamental Astronomy) software collection.
7361 *
7362 *<p>Status: support function.
7363 *
7364 *<!-- Given: -->
7365 * @param date1 double TDB date (Note 1)
7366 * @param date2 double TDB date (Note 1)
7367 *
7368 *<!-- Returned: -->
7369 * @param pvh double[2][3] <u>returned</u> heliocentric Earth position/velocity (AU, AU/d)
7370 * @param pvb double[2][3] <u>returned</u> barycentric Earth position/velocity (AU, AU/d)
7371 *
7372 * <!-- Returned (function value): -->
7373 * @return int status: 0 = OK
7374 * +1 = warning: date outside
7375 * the range 1900-2100 AD
7376 *
7377 * <p>Notes:
7378 * <ol>
7379 *
7380 * <li> The TDB date date1+date2 is a Julian Date, apportioned in any
7381 * convenient way between the two arguments. For example,
7382 * JD(TDB)=2450123.7 could be expressed in any of these ways, among
7383 * others:
7384 *<pre>
7385 * date1 date2
7386 *
7387 * 2450123.7 0.0 (JD method)
7388 * 2451545.0 -1421.3 (J2000 method)
7389 * 2400000.5 50123.2 (MJD method)
7390 * 2450123.5 0.2 (date & time method)
7391 *</pre>
7392 * The JD method is the most natural and convenient to use in cases
7393 * where the loss of several decimal digits of resolution is
7394 * acceptable. The J2000 method is best matched to the way the
7395 * argument is handled internally and will deliver the optimum
7396 * resolution. The MJD method and the date & time methods are both
7397 * good compromises between resolution and convenience. However,
7398 * the accuracy of the result is more likely to be limited by the
7399 * algorithm itself than the way the date has been expressed.
7400 *
7401 * n.b. TT can be used instead of TDB in most applications.
7402 *
7403 * <li> On return, the arrays pvh and pvb contain the following:
7404 *
7405 * pvh[0][0] x }
7406 * pvh[0][1] y } heliocentric position, AU
7407 * pvh[0][2] z }
7408 *
7409 * pvh[1][0] xdot }
7410 * pvh[1][1] ydot } heliocentric velocity, AU/d
7411 * pvh[1][2] zdot }
7412 *
7413 * pvb[0][0] x }
7414 * pvb[0][1] y } barycentric position, AU
7415 * pvb[0][2] z }
7416 *
7417 * pvb[1][0] xdot }
7418 * pvb[1][1] ydot } barycentric velocity, AU/d
7419 * pvb[1][2] zdot }
7420 *
7421 * The vectors are with respect to the Barycentric Celestial
7422 * Reference System. The time unit is one day in TDB.
7423 *
7424 * <li> The function is a SIMPLIFIED SOLUTION from the planetary theory
7425 * VSOP2000 (X. Moisson, P. Bretagnon, 2001, Celes. Mechanics &
7426 * Dyn. Astron., 80, 3/4, 205-213) and is an adaptation of original
7427 * Fortran code supplied by P. Bretagnon (private comm., 2000).
7428 *
7429 * <li> Comparisons over the time span 1900-2100 with this simplified
7430 * solution and the JPL DE405 ephemeris give the following results:
7431 *
7432 * RMS max
7433 * Heliocentric:
7434 * position error 3.7 11.2 km
7435 * velocity error 1.4 5.0 mm/s
7436 *
7437 * Barycentric:
7438 * position error 4.6 13.4 km
7439 * velocity error 1.4 4.9 mm/s
7440 *
7441 * Comparisons with the JPL DE406 ephemeris show that by 1800 and
7442 * 2200 the position errors are approximately double their 1900-2100
7443 * size. By 1500 and 2500 the deterioration is a factor of 10 and
7444 * by 1000 and 3000 a factor of 60. The velocity accuracy falls off
7445 * at about half that rate.
7446 *
7447 * <li> It is permissible to use the same array for pvh and pvb, which
7448 * will receive the barycentric values.
7449 *</ol>
7450 *@version 2008 November 18
7451 *
7452 * @since Release 20101201
7453 *
7454 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
7455 */
7456 public static int jauEpv00(final double date1, final double date2,
7457 double pvh[][], double pvb[][])
7458 {
7459 /*
7460 * Matrix elements for orienting the analytical model to DE405.
7461 *
7462 * The corresponding Euler angles are:
7463 *
7464 * d ' "
7465 * 1st rotation - 23 26 21.4091 about the x-axis (obliquity)
7466 * 2nd rotation + 0.0475 about the z-axis (RA offset)
7467 *
7468 * These were obtained empirically, by comparisons with DE405 over
7469 * 1900-2100.
7470 */
7471 final double am12 = 0.000000211284,
7472 am13 = -0.000000091603,
7473 am21 = -0.000000230286,
7474 am22 = 0.917482137087,
7475 am23 = -0.397776982902,
7476 am32 = 0.397776982902,
7477 am33 = 0.917482137087;
7478
7479
7480
7481
7482 /* Pointers to coefficient arrays, in x,y,z sets */
7483 final double ce0[][] = { Ephemeris.e0x, Ephemeris.e0y, Ephemeris.e0z },
7484 ce1[][] = { Ephemeris.e1x, Ephemeris.e1y, Ephemeris.e1z },
7485 ce2[][] = { Ephemeris.e2x, Ephemeris.e2y, Ephemeris.e2z },
7486 cs0[][] = { Ephemeris.s0x, Ephemeris.s0y, Ephemeris.s0z },
7487 cs1[][] = { Ephemeris.s1x, Ephemeris.s1y, Ephemeris.s1z },
7488 cs2[][] = { Ephemeris.s2x, Ephemeris.s2y, Ephemeris.s2z };
7489 /* Numbers of terms for each component of the model, in x,y,z sets */
7490 final int ne0[] = {Ephemeris.e0x.length/3,
7491 Ephemeris.e0y.length/3,
7492 Ephemeris.e0z.length/3 },
7493 ne1[] = {Ephemeris.e1x.length/3,
7494 Ephemeris.e1y.length/3,
7495 Ephemeris.e1z.length/3 },
7496 ne2[] = {Ephemeris.e2x.length/3,
7497 Ephemeris.e2y.length/3,
7498 Ephemeris.e2z.length/3 },
7499 ns0[] = {Ephemeris.s0x.length/3,
7500 Ephemeris.s0y.length/3,
7501 Ephemeris.s0z.length/3 },
7502 ns1[] = {Ephemeris.s1x.length/3,
7503 Ephemeris.s1y.length/3,
7504 Ephemeris.s1z.length/3 },
7505 ns2[] = {Ephemeris.s2x.length/3,
7506 Ephemeris.s2y.length/3,
7507 Ephemeris.s2z.length/3 };
7508 int nterms;
7509
7510 /* Miscellaneous */
7511 int jstat, i, j;
7512 double t, t2, xyz, xyzd, a, b, c, ct, p, cp,
7513 ph[] = new double[3], vh[] = new double[3], pb[] = new double[3], vb[] = new double[3], x, y, z;
7514
7515 /*--------------------------------------------------------------------*/
7516
7517 /* Time since reference epoch, Julian years. */
7518 t = ((date1 - DJ00) + date2) / DJY;
7519 t2 = t*t;
7520
7521 /* Set status. */
7522 jstat = abs(t) <= 100.0 ? 0 : 1;
7523
7524 /* X then Y then Z. */
7525 for (i = 0; i < 3; i++) {
7526
7527 /* Initialize position and velocity component. */
7528 xyz = 0.0;
7529 xyzd = 0.0;
7530
7531 /* ------------------------------------------------ */
7532 /* Obtain component of Sun to Earth ecliptic vector */
7533 /* ------------------------------------------------ */
7534
7535 /* Sun to Earth, T^0 terms. */
7536 nterms = ne0[i];
7537 int idx;
7538 for (j = 0, idx=0; j < nterms; j++) {
7539 a = ce0[i][idx++];
7540 b = ce0[i][idx++];
7541 c = ce0[i][idx++];
7542 p = b + c*t;
7543 xyz += a*cos(p);
7544 xyzd -= a*c*sin(p);
7545 }
7546
7547 /* Sun to Earth, T^1 terms. */
7548 nterms = ne1[i];
7549 for (j = 0, idx= 0; j < nterms; j++) {
7550 a = ce1[i][idx++];
7551 b = ce1[i][idx++];
7552 c = ce1[i][idx++];
7553 ct = c*t;
7554 p = b + ct;
7555 cp = cos(p);
7556 xyz += a*t*cp;
7557 xyzd += a*( cp - ct*sin(p) );
7558 }
7559
7560 /* Sun to Earth, T^2 terms. */
7561 nterms = ne2[i];
7562 for (j = 0, idx = 0; j < nterms; j++) {
7563 a = ce2[i][idx++];
7564 b = ce2[i][idx++];
7565 c = ce2[i][idx++];
7566 ct = c*t;
7567 p = b + ct;
7568 cp = cos(p);
7569 xyz += a*t2*cp;
7570 xyzd += a*t*( 2.0*cp - ct*sin(p) );
7571 }
7572
7573 /* Heliocentric Earth position and velocity component. */
7574 ph[i] = xyz;
7575 vh[i] = xyzd / DJY;
7576
7577 /* ------------------------------------------------ */
7578 /* Obtain component of SSB to Earth ecliptic vector */
7579 /* ------------------------------------------------ */
7580
7581 /* SSB to Sun, T^0 terms. */
7582 nterms = ns0[i];
7583 for (j = 0, idx = 0; j < nterms; j++) {
7584 a = cs0[i][idx++];
7585 b = cs0[i][idx++];
7586 c = cs0[i][idx++];
7587 p = b + c*t;
7588 xyz += a*cos(p);
7589 xyzd -= a*c*sin(p);
7590 }
7591
7592 /* SSB to Sun, T^1 terms. */
7593 nterms = ns1[i];
7594 for (j = 0, idx = 0; j < nterms; j++) {
7595 a = cs1[i][idx++];
7596 b = cs1[i][idx++];
7597 c = cs1[i][idx++];
7598 ct = c*t;
7599 p = b + ct;
7600 cp = cos(p);
7601 xyz += a*t*cp;
7602 xyzd += a*(cp - ct*sin(p));
7603 }
7604
7605 /* SSB to Sun, T^2 terms. */
7606 nterms = ns2[i];
7607 for (j = 0, idx = 0; j < nterms; j++) {
7608 a = cs2[i][idx++];
7609 b = cs2[i][idx++];
7610 c = cs2[i][idx++];
7611 ct = c*t;
7612 p = b + ct;
7613 cp = cos(p);
7614 xyz += a*t2*cp;
7615 xyzd += a*t*(2.0*cp - ct*sin(p));
7616 }
7617
7618 /* Barycentric Earth position and velocity component. */
7619 pb[i] = xyz;
7620 vb[i] = xyzd / DJY;
7621
7622 /* Next Cartesian component. */
7623 }
7624
7625 /* Rotate from ecliptic to BCRS coordinates. */
7626
7627 x = ph[0];
7628 y = ph[1];
7629 z = ph[2];
7630 pvh[0][0] = x + am12*y + am13*z;
7631 pvh[0][1] = am21*x + am22*y + am23*z;
7632 pvh[0][2] = am32*y + am33*z;
7633
7634 x = vh[0];
7635 y = vh[1];
7636 z = vh[2];
7637 pvh[1][0] = x + am12*y + am13*z;
7638 pvh[1][1] = am21*x + am22*y + am23*z;
7639 pvh[1][2] = am32*y + am33*z;
7640
7641 x = pb[0];
7642 y = pb[1];
7643 z = pb[2];
7644 pvb[0][0] = x + am12*y + am13*z;
7645 pvb[0][1] = am21*x + am22*y + am23*z;
7646 pvb[0][2] = am32*y + am33*z;
7647
7648 x = vb[0];
7649 y = vb[1];
7650 z = vb[2];
7651 pvb[1][0] = x + am12*y + am13*z;
7652 pvb[1][1] = am21*x + am22*y + am23*z;
7653 pvb[1][2] = am32*y + am33*z;
7654
7655 /* Return the status. */
7656 return jstat;
7657
7658 }
7659
7660
7661 /**
7662 * Equation of the equinoxes, IAU 1994 model.
7663 *
7664 *<p>This function is derived from the International Astronomical Union's
7665 * SOFA (Standards Of Fundamental Astronomy) software collection.
7666 *
7667 *<p>Status: canonical model.
7668 *
7669 *<!-- Given: -->
7670 * @param date1 double TDB date (Note 1)
7671 * @param date2 double TDB date (Note 1)
7672 *
7673 * <!-- Returned (function value): -->
7674 * @return double equation of the equinoxes (Note 2)
7675 *
7676 * <p>Notes:
7677 * <ol>
7678 *
7679 * <li> The date date1+date2 is a Julian Date, apportioned in any
7680 * convenient way between the two arguments. For example,
7681 * JD(TT)=2450123.7 could be expressed in any of these ways,
7682 * among others:
7683 *<pre>
7684 * date1 date2
7685 *
7686 * 2450123.7 0.0 (JD method)
7687 * 2451545.0 -1421.3 (J2000 method)
7688 * 2400000.5 50123.2 (MJD method)
7689 * 2450123.5 0.2 (date & time method)
7690 *</pre>
7691 * The JD method is the most natural and convenient to use in
7692 * cases where the loss of several decimal digits of resolution
7693 * is acceptable. The J2000 method is best matched to the way
7694 * the argument is handled internally and will deliver the
7695 * optimum resolution. The MJD method and the date & time methods
7696 * are both good compromises between resolution and convenience.
7697 *
7698 * <li> The result, which is in radians, operates in the following sense:
7699 *
7700 * Greenwich apparent ST = GMST + equation of the equinoxes
7701 *</ol>
7702 *<p>Called:<ul>
7703 * <li>{@link #jauNut80} nutation, IAU 1980
7704 * <li>{@link #jauObl80} mean obliquity, IAU 1980
7705 * </ul>
7706 *<p>References:
7707 *
7708 * <p>IAU Resolution C7, Recommendation 3 (1994).
7709 *
7710 * <p>Capitaine, N. & Gontier, A.-M., 1993, Astron. Astrophys., 275,
7711 * 645-650.
7712 *
7713 *@version 2008 May 24
7714 *
7715 * @since Release 20101201
7716 *
7717 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
7718 */
7719 public static double jauEqeq94(double date1, double date2)
7720 {
7721 double t, om, eps0, ee;
7722
7723
7724 /* Interval between fundamental epoch J2000.0 and given date (JC). */
7725 t = ((date1 - DJ00) + date2) / DJC;
7726
7727 /* Longitude of the mean ascending node of the lunar orbit on the */
7728 /* ecliptic, measured from the mean equinox of date. */
7729 om = jauAnpm((450160.280 + (-482890.539
7730 + (7.455 + 0.008 * t) * t) * t) * DAS2R
7731 + fmod(-5.0 * t, 1.0) * D2PI);
7732
7733 /* Nutation components and mean obliquity. */
7734 NutationTerms nt = jauNut80(date1, date2);
7735 eps0 = jauObl80(date1, date2);
7736
7737 /* Equation of the equinoxes. */
7738 ee = nt.dpsi*cos(eps0) + DAS2R*(0.00264*sin(om) + 0.000063*sin(om+om));
7739
7740 return ee;
7741
7742 }
7743
7744
7745 /**
7746 * Earth rotation angle (IAU 2000 model).
7747 *
7748 *<p>This function is derived from the International Astronomical Union's
7749 * SOFA (Standards Of Fundamental Astronomy) software collection.
7750 *
7751 *<p>Status: canonical model.
7752 *
7753 *<!-- Given: -->
7754 * @param dj1 double UT1 as a 2-part Julian Date (see note)
7755 * @param dj2 double UT1 as a 2-part Julian Date (see note)
7756 *
7757 * <!-- Returned (function value): -->
7758 * @return double Earth rotation angle (radians), range 0-2pi
7759 *
7760 * <p>Notes:
7761 * <ol>
7762 *
7763 * <li> The UT1 date dj1+dj2 is a Julian Date, apportioned in any
7764 * convenient way between the arguments dj1 and dj2. For example,
7765 * JD(UT1)=2450123.7 could be expressed in any of these ways,
7766 * among others:
7767 *<pre>
7768 * dj1 dj2
7769 *
7770 * 2450123.7 0.0 (JD method)
7771 * 2451545.0 -1421.3 (J2000 method)
7772 * 2400000.5 50123.2 (MJD method)
7773 * 2450123.5 0.2 (date & time method)
7774 *</pre>
7775 * The JD method is the most natural and convenient to use in
7776 * cases where the loss of several decimal digits of resolution
7777 * is acceptable. The J2000 and MJD methods are good compromises
7778 * between resolution and convenience. The date & time method is
7779 * best matched to the algorithm used: maximum precision is
7780 * delivered when the dj1 argument is for 0hrs UT1 on the day in
7781 * question and the dj2 argument lies in the range 0 to 1, or vice
7782 * versa.
7783 *
7784 * <li> The algorithm is adapted from Expression 22 of Capitaine et al.
7785 * 2000. The time argument has been expressed in days directly,
7786 * and, to retain precision, integer contributions have been
7787 * eliminated. The same formulation is given in IERS Conventions
7788 * (2003), Chap. 5, Eq. 14.
7789 *</ol>
7790 *<p>Called:<ul>
7791 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
7792 * </ul>
7793 *<p>References:
7794 *
7795 * <p>Capitaine N., Guinot B. and McCarthy D.D, 2000, Astron.
7796 * Astrophys., 355, 398-405.
7797 *
7798 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
7799 * IERS Technical Note No. 32, BKG (2004)
7800 *
7801 *@version 2008 May 24
7802 *
7803 * @since Release 20101201
7804 *
7805 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
7806 */
7807 public static double jauEra00(double dj1, double dj2)
7808 {
7809 double d1, d2, t, f, theta;
7810
7811
7812 /* Days since fundamental epoch. */
7813 if (dj1 < dj2) {
7814 d1 = dj1;
7815 d2 = dj2;
7816 } else {
7817 d1 = dj2;
7818 d2 = dj1;
7819 }
7820 t = d1 + (d2- DJ00);
7821
7822 /* Fractional part of T (days). */
7823 f = fmod(d1, 1.0) + fmod(d2, 1.0);
7824
7825 /* Earth rotation angle at this UT1. */
7826 theta = jauAnp(D2PI * (f + 0.7790572732640
7827 + 0.00273781191135448 * t));
7828
7829 return theta;
7830
7831 }
7832
7833
7834 /**
7835 * Fundamental argument, IERS Conventions (2003):
7836 * mean elongation of the Moon from the Sun.
7837 *
7838 *<p>This function is derived from the International Astronomical Union's
7839 * SOFA (Standards Of Fundamental Astronomy) software collection.
7840 *
7841 *<p>Status: canonical model.
7842 *
7843 *<!-- Given: -->
7844 * @param t double TDB, Julian centuries since J2000.0 (Note 1)
7845 *
7846 * <!-- Returned (function value): -->
7847 * @return double D, radians (Note 2)
7848 *
7849 * <p>Notes:
7850 * <ol>
7851 *
7852 * <li> Though t is strictly TDB, it is usually more convenient to use
7853 * TT, which makes no significant difference.
7854 *
7855 * <li> The expression used is as adopted in IERS Conventions (2003) and
7856 * is from Simon et al. (1994).
7857 *</ol>
7858 *<p>References:
7859 *
7860 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
7861 * IERS Technical Note No. 32, BKG (2004)
7862 *
7863 * <p>Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
7864 * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
7865 *
7866 *@version 2009 December 16
7867 *
7868 * @since Release 20101201
7869 *
7870 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
7871 */
7872 public static double jauFad03(double t)
7873 {
7874 double a;
7875
7876
7877 /* Mean elongation of the Moon from the Sun (IERS Conventions 2003). */
7878 a = fmod( 1072260.703692 +
7879 t * ( 1602961601.2090 +
7880 t * ( - 6.3706 +
7881 t * ( 0.006593 +
7882 t * ( - 0.00003169 ) ) ) ), TURNAS ) * DAS2R;
7883
7884 return a;
7885
7886 }
7887
7888
7889 /**
7890 * Fundamental argument, IERS Conventions (2003):
7891 * mean longitude of Earth.
7892 *
7893 *<p>This function is derived from the International Astronomical Union's
7894 * SOFA (Standards Of Fundamental Astronomy) software collection.
7895 *
7896 *<p>Status: canonical model.
7897 *
7898 *<!-- Given: -->
7899 * @param t double TDB, Julian centuries since J2000.0 (Note 1)
7900 *
7901 * <!-- Returned (function value): -->
7902 * @return double mean longitude of Earth, radians (Note 2)
7903 *
7904 * <p>Notes:
7905 * <ol>
7906 *
7907 * <li> Though t is strictly TDB, it is usually more convenient to use
7908 * TT, which makes no significant difference.
7909 *
7910 * <li> The expression used is as adopted in IERS Conventions (2003) and
7911 * comes from Souchay et al. (1999) after Simon et al. (1994).
7912 *</ol>
7913 *<p>References:
7914 *
7915 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
7916 * IERS Technical Note No. 32, BKG (2004)
7917 *
7918 * <p>Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
7919 * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
7920 *
7921 * <p>Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
7922 * Astron.Astrophys.Supp.Ser. 135, 111
7923 *
7924 *@version 2009 December 16
7925 *
7926 * @since Release 20101201
7927 *
7928 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
7929 */
7930 public static double jauFae03(double t)
7931 {
7932 double a;
7933
7934
7935 /* Mean longitude of Earth (IERS Conventions 2003). */
7936 a = fmod(1.753470314 + 628.3075849991 * t, D2PI);
7937
7938 return a;
7939
7940 }
7941
7942
7943 /**
7944 * Fundamental argument, IERS Conventions (2003):
7945 * mean longitude of the Moon minus mean longitude of the ascending
7946 * node.
7947 *
7948 *<p>This function is derived from the International Astronomical Union's
7949 * SOFA (Standards Of Fundamental Astronomy) software collection.
7950 *
7951 *<p>Status: canonical model.
7952 *
7953 *<!-- Given: -->
7954 * @param t double TDB, Julian centuries since J2000.0 (Note 1)
7955 *
7956 * <!-- Returned (function value): -->
7957 * @return double F, radians (Note 2)
7958 *
7959 * <p>Notes:
7960 * <ol>
7961 *
7962 * <li> Though t is strictly TDB, it is usually more convenient to use
7963 * TT, which makes no significant difference.
7964 *
7965 * <li> The expression used is as adopted in IERS Conventions (2003) and
7966 * is from Simon et al. (1994).
7967 *</ol>
7968 *<p>References:
7969 *
7970 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
7971 * IERS Technical Note No. 32, BKG (2004)
7972 *
7973 * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
7974 * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
7975 *
7976 *@version 2009 December 16
7977 *
7978 * @since Release 20101201
7979 *
7980 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
7981 */
7982 public static double jauFaf03(double t)
7983 {
7984 double a;
7985
7986
7987 /* Mean longitude of the Moon minus that of the ascending node */
7988 /* (IERS Conventions 2003). */
7989 a = fmod( 335779.526232 +
7990 t * ( 1739527262.8478 +
7991 t * ( - 12.7512 +
7992 t * ( - 0.001037 +
7993 t * ( 0.00000417 ) ) ) ), TURNAS ) * DAS2R;
7994
7995 return a;
7996
7997
7998 }
7999
8000
8001 /**
8002 * Fundamental argument, IERS Conventions (2003):
8003 * mean longitude of Jupiter.
8004 *
8005 *<p>This function is derived from the International Astronomical Union's
8006 * SOFA (Standards Of Fundamental Astronomy) software collection.
8007 *
8008 *<p>Status: canonical model.
8009 *
8010 *<!-- Given: -->
8011 * @param t double TDB, Julian centuries since J2000.0 (Note 1)
8012 *
8013 * <!-- Returned (function value): -->
8014 * @return double mean longitude of Jupiter, radians (Note 2)
8015 *
8016 * <p>Notes:
8017 * <ol>
8018 *
8019 * <li> Though t is strictly TDB, it is usually more convenient to use
8020 * TT, which makes no significant difference.
8021 *
8022 * <li> The expression used is as adopted in IERS Conventions (2003) and
8023 * comes from Souchay et al. (1999) after Simon et al. (1994).
8024 *</ol>
8025 *<p>References:
8026 *
8027 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8028 * IERS Technical Note No. 32, BKG (2004)
8029 *
8030 * <p>Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8031 * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8032 *
8033 * <p>Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
8034 * Astron.Astrophys.Supp.Ser. 135, 111
8035 *
8036 *@version 2009 December 16
8037 *
8038 * @since Release 20101201
8039 *
8040 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8041 */
8042 public static double jauFaju03(double t)
8043 {
8044 double a;
8045
8046
8047 /* Mean longitude of Jupiter (IERS Conventions 2003). */
8048 a = fmod(0.599546497 + 52.9690962641 * t, D2PI);
8049
8050 return a;
8051
8052 }
8053
8054
8055 /**
8056 * Fundamental argument, IERS Conventions (2003):
8057 * mean anomaly of the Moon.
8058 *
8059 *<p>This function is derived from the International Astronomical Union's
8060 * SOFA (Standards Of Fundamental Astronomy) software collection.
8061 *
8062 *<p>Status: canonical model.
8063 *
8064 *<!-- Given: -->
8065 * @param t double TDB, Julian centuries since J2000.0 (Note 1)
8066 *
8067 * <!-- Returned (function value): -->
8068 * @return double l, radians (Note 2)
8069 *
8070 * <p>Notes:
8071 * <ol>
8072 *
8073 * <li> Though t is strictly TDB, it is usually more convenient to use
8074 * TT, which makes no significant difference.
8075 *
8076 * <li> The expression used is as adopted in IERS Conventions (2003) and
8077 * is from Simon et al. (1994).
8078 *</ol>
8079 *<p>References:
8080 *
8081 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8082 * IERS Technical Note No. 32, BKG (2004)
8083 *
8084 * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8085 * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8086 *
8087 *@version 2009 December 16
8088 *
8089 * @since Release 20101201
8090 *
8091 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8092 */
8093 public static double jauFal03(double t)
8094 {
8095 double a;
8096
8097
8098 /* Mean anomaly of the Moon (IERS Conventions 2003). */
8099 a = fmod( 485868.249036 +
8100 t * ( 1717915923.2178 +
8101 t * ( 31.8792 +
8102 t * ( 0.051635 +
8103 t * ( - 0.00024470 ) ) ) ), TURNAS ) * DAS2R;
8104
8105 return a;
8106
8107 }
8108
8109
8110 /**
8111 * Fundamental argument, IERS Conventions (2003):
8112 * mean anomaly of the Sun.
8113 *
8114 *<p>This function is derived from the International Astronomical Union's
8115 * SOFA (Standards Of Fundamental Astronomy) software collection.
8116 *
8117 *<p>Status: canonical model.
8118 *
8119 *<!-- Given: -->
8120 * @param t double TDB, Julian centuries since J2000.0 (Note 1)
8121 *
8122 * <!-- Returned (function value): -->
8123 * @return double l', radians (Note 2)
8124 *
8125 * <p>Notes:
8126 * <ol>
8127 *
8128 * <li> Though t is strictly TDB, it is usually more convenient to use
8129 * TT, which makes no significant difference.
8130 *
8131 * <li> The expression used is as adopted in IERS Conventions (2003) and
8132 * is from Simon et al. (1994).
8133 *</ol>
8134 *<p>References:
8135 *
8136 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8137 * IERS Technical Note No. 32, BKG (2004)
8138 *
8139 * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8140 * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8141 *
8142 *@version 2009 December 16
8143 *
8144 * @since Release 20101201
8145 *
8146 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8147 */
8148 public static double jauFalp03(double t)
8149 {
8150 double a;
8151
8152
8153 /* Mean anomaly of the Sun (IERS Conventions 2003). */
8154 a = fmod( 1287104.793048 +
8155 t * ( 129596581.0481 +
8156 t * ( - 0.5532 +
8157 t * ( 0.000136 +
8158 t * ( - 0.00001149 ) ) ) ), TURNAS ) * DAS2R;
8159
8160 return a;
8161
8162 }
8163
8164
8165 /**
8166 * Fundamental argument, IERS Conventions (2003):
8167 * mean longitude of Mars.
8168 *
8169 *<p>This function is derived from the International Astronomical Union's
8170 * SOFA (Standards Of Fundamental Astronomy) software collection.
8171 *
8172 *<p>Status: canonical model.
8173 *
8174 *<!-- Given: -->
8175 * @param t double TDB, Julian centuries since J2000.0 (Note 1)
8176 *
8177 * <!-- Returned (function value): -->
8178 * @return double mean longitude of Mars, radians (Note 2)
8179 *
8180 * <p>Notes:
8181 * <ol>
8182 *
8183 * <li> Though t is strictly TDB, it is usually more convenient to use
8184 * TT, which makes no significant difference.
8185 *
8186 * <li> The expression used is as adopted in IERS Conventions (2003) and
8187 * comes from Souchay et al. (1999) after Simon et al. (1994).
8188 *</ol>
8189 *<p>References:
8190 *
8191 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8192 * IERS Technical Note No. 32, BKG (2004)
8193 *
8194 * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8195 * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8196 *
8197 * Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
8198 * Astron.Astrophys.Supp.Ser. 135, 111
8199 *
8200 *@version 2009 December 16
8201 *
8202 * @since Release 20101201
8203 *
8204 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8205 */
8206 public static double jauFama03(double t)
8207 {
8208 double a;
8209
8210
8211 /* Mean longitude of Mars (IERS Conventions 2003). */
8212 a = fmod(6.203480913 + 334.0612426700 * t, D2PI);
8213
8214 return a;
8215
8216 }
8217
8218
8219 /**
8220 * Fundamental argument, IERS Conventions (2003):
8221 * mean longitude of Mercury.
8222 *
8223 *<p>This function is derived from the International Astronomical Union's
8224 * SOFA (Standards Of Fundamental Astronomy) software collection.
8225 *
8226 *<p>Status: canonical model.
8227 *
8228 *<!-- Given: -->
8229 * @param t double TDB, Julian centuries since J2000.0 (Note 1)
8230 *
8231 * <!-- Returned (function value): -->
8232 * @return double mean longitude of Mercury, radians (Note 2)
8233 *
8234 * <p>Notes:
8235 * <ol>
8236 *
8237 * <li> Though t is strictly TDB, it is usually more convenient to use
8238 * TT, which makes no significant difference.
8239 *
8240 * <li> The expression used is as adopted in IERS Conventions (2003) and
8241 * comes from Souchay et al. (1999) after Simon et al. (1994).
8242 *</ol>
8243 *<p>References:
8244 *
8245 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8246 * IERS Technical Note No. 32, BKG (2004)
8247 *
8248 * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8249 * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8250 *
8251 * Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
8252 * Astron.Astrophys.Supp.Ser. 135, 111
8253 *
8254 *@version 2009 December 16
8255 *
8256 * @since Release 20101201
8257 *
8258 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8259 */
8260 public static double jauFame03(double t)
8261 {
8262 double a;
8263
8264
8265 /* Mean longitude of Mercury (IERS Conventions 2003). */
8266 a = fmod(4.402608842 + 2608.7903141574 * t, D2PI);
8267
8268 return a;
8269
8270 }
8271
8272
8273
8274 /**
8275 * Fundamental argument, IERS Conventions (2003):
8276 * mean longitude of Neptune.
8277 *
8278 *<p>This function is derived from the International Astronomical Union's
8279 * SOFA (Standards Of Fundamental Astronomy) software collection.
8280 *
8281 *<p>Status: canonical model.
8282 *
8283 *<!-- Given: -->
8284 * @param t double TDB, Julian centuries since J2000.0 (Note 1)
8285 *
8286 * <!-- Returned (function value): -->
8287 * @return double mean longitude of Neptune, radians (Note 2)
8288 *
8289 * <p>Notes:
8290 * <ol>
8291 *
8292 * <li> Though t is strictly TDB, it is usually more convenient to use
8293 * TT, which makes no significant difference.
8294 *
8295 * <li> The expression used is as adopted in IERS Conventions (2003) and
8296 * is adapted from Simon et al. (1994).
8297 *</ol>
8298 *<p>References:
8299 *
8300 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8301 * IERS Technical Note No. 32, BKG (2004)
8302 *
8303 * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8304 * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8305 *
8306 *@version 2009 December 16
8307 *
8308 * @since Release 20101201
8309 *
8310 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8311 */
8312 public static double jauFane03(double t)
8313 {
8314 double a;
8315
8316
8317 /* Mean longitude of Neptune (IERS Conventions 2003). */
8318 a = fmod(5.311886287 + 3.8133035638 * t, D2PI);
8319
8320 return a;
8321
8322 }
8323
8324
8325 /**
8326 * Fundamental argument, IERS Conventions (2003):
8327 * mean longitude of the Moon's ascending node.
8328 *
8329 *<p>This function is derived from the International Astronomical Union's
8330 * SOFA (Standards Of Fundamental Astronomy) software collection.
8331 *
8332 *<p>Status: canonical model.
8333 *
8334 *<!-- Given: -->
8335 * @param t double TDB, Julian centuries since J2000.0 (Note 1)
8336 *
8337 * <!-- Returned (function value): -->
8338 * @return double Omega, radians (Note 2)
8339 *
8340 * <p>Notes:
8341 * <ol>
8342 *
8343 * <li> Though t is strictly TDB, it is usually more convenient to use
8344 * TT, which makes no significant difference.
8345 *
8346 * <li> The expression used is as adopted in IERS Conventions (2003) and
8347 * is from Simon et al. (1994).
8348 *</ol>
8349 *<p>References:
8350 *
8351 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8352 * IERS Technical Note No. 32, BKG (2004)
8353 *
8354 * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8355 * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8356 *
8357 *@version 2009 December 16
8358 *
8359 * @since Release 20101201
8360 *
8361 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8362 */
8363 public static double jauFaom03(double t)
8364 {
8365 double a;
8366
8367
8368 /* Mean longitude of the Moon's ascending node */
8369 /* (IERS Conventions 2003). */
8370 a = fmod( 450160.398036 +
8371 t * ( - 6962890.5431 +
8372 t * ( 7.4722 +
8373 t * ( 0.007702 +
8374 t * ( - 0.00005939 ) ) ) ), TURNAS ) * DAS2R;
8375
8376 return a;
8377
8378 }
8379
8380
8381 /**
8382 * Fundamental argument, IERS Conventions (2003):
8383 * general accumulated precession in longitude.
8384 *
8385 *<p>This function is derived from the International Astronomical Union's
8386 * SOFA (Standards Of Fundamental Astronomy) software collection.
8387 *
8388 *<p>Status: canonical model.
8389 *
8390 *<!-- Given: -->
8391 * @param t double TDB, Julian centuries since J2000.0 (Note 1)
8392 *
8393 * <!-- Returned (function value): -->
8394 * @return double general precession in longitude, radians (Note 2)
8395 *
8396 * <p>Notes:
8397 * <ol>
8398 *
8399 * <li> Though t is strictly TDB, it is usually more convenient to use
8400 * TT, which makes no significant difference.
8401 *
8402 * <li> The expression used is as adopted in IERS Conventions (2003). It
8403 * is taken from Kinoshita & Souchay (1990) and comes originally
8404 * from Lieske et al. (1977).
8405 *</ol>
8406 *<p>References:
8407 *
8408 * Kinoshita, H. and Souchay J. 1990, Celest.Mech. and Dyn.Astron.
8409 * 48, 187
8410 *
8411 * <p>Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977,
8412 * Astron.Astrophys. 58, 1-16
8413 *
8414 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8415 * IERS Technical Note No. 32, BKG (2004)
8416 *
8417 *@version 2009 December 16
8418 *
8419 * @since Release 20101201
8420 *
8421 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8422 */
8423 public static double jauFapa03(double t)
8424 {
8425 double a;
8426
8427
8428 /* General accumulated precession in longitude. */
8429 a = (0.024381750 + 0.00000538691 * t) * t;
8430
8431 return a;
8432
8433 }
8434
8435
8436 /**
8437 * Fundamental argument, IERS Conventions (2003):
8438 * mean longitude of Saturn.
8439 *
8440 *<p>This function is derived from the International Astronomical Union's
8441 * SOFA (Standards Of Fundamental Astronomy) software collection.
8442 *
8443 *<p>Status: canonical model.
8444 *
8445 *<!-- Given: -->
8446 * @param t double TDB, Julian centuries since J2000.0 (Note 1)
8447 *
8448 * <!-- Returned (function value): -->
8449 * @return double mean longitude of Saturn, radians (Note 2)
8450 *
8451 * <p>Notes:
8452 * <ol>
8453 *
8454 * <li> Though t is strictly TDB, it is usually more convenient to use
8455 * TT, which makes no significant difference.
8456 *
8457 * <li> The expression used is as adopted in IERS Conventions (2003) and
8458 * comes from Souchay et al. (1999) after Simon et al. (1994).
8459 *</ol>
8460 *<p>References:
8461 *
8462 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8463 * IERS Technical Note No. 32, BKG (2004)
8464 *
8465 * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8466 * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8467 *
8468 * Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
8469 * Astron.Astrophys.Supp.Ser. 135, 111
8470 *
8471 *@version 2009 December 16
8472 *
8473 * @since Release 20101201
8474 *
8475 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8476 */
8477 public static double jauFasa03(double t)
8478 {
8479 double a;
8480
8481
8482 /* Mean longitude of Saturn (IERS Conventions 2003). */
8483 a = fmod(0.874016757 + 21.3299104960 * t, D2PI);
8484
8485 return a;
8486
8487 }
8488
8489
8490 /**
8491 * Fundamental argument, IERS Conventions (2003):
8492 * mean longitude of Uranus.
8493 *
8494 *<p>This function is derived from the International Astronomical Union's
8495 * SOFA (Standards Of Fundamental Astronomy) software collection.
8496 *
8497 *<p>Status: canonical model.
8498 *
8499 *<!-- Given: -->
8500 * @param t double TDB, Julian centuries since J2000.0 (Note 1)
8501 *
8502 * Returned (function value):
8503 * double mean longitude of Uranus, radians (Note 2)
8504 *
8505 * <p>Notes:
8506 * <ol>
8507 *
8508 * <li> Though t is strictly TDB, it is usually more convenient to use
8509 * TT, which makes no significant difference.
8510 *
8511 * <li> The expression used is as adopted in IERS Conventions (2003) and
8512 * is adapted from Simon et al. (1994).
8513 *</ol>
8514 *<p>References:
8515 *
8516 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8517 * IERS Technical Note No. 32, BKG (2004)
8518 *
8519 * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8520 * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8521 *
8522 *@version 2009 December 16
8523 *
8524 * @since Release 20101201
8525 *
8526 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8527 */
8528 public static double jauFaur03(double t)
8529 {
8530 double a;
8531
8532
8533 /* Mean longitude of Uranus (IERS Conventions 2003). */
8534 a = fmod(5.481293872 + 7.4781598567 * t, D2PI);
8535
8536 return a;
8537
8538 }
8539
8540
8541 /**
8542 * Fundamental argument, IERS Conventions (2003):
8543 * mean longitude of Venus.
8544 *
8545 *<p>This function is derived from the International Astronomical Union's
8546 * SOFA (Standards Of Fundamental Astronomy) software collection.
8547 *
8548 *<p>Status: canonical model.
8549 *
8550 *<!-- Given: -->
8551 * @param t double TDB, Julian centuries since J2000.0 (Note 1)
8552 *
8553 * <!-- Returned (function value): -->
8554 * @return double mean longitude of Venus, radians (Note 2)
8555 *
8556 * <p>Notes:
8557 * <ol>
8558 *
8559 * <li> Though t is strictly TDB, it is usually more convenient to use
8560 * TT, which makes no significant difference.
8561 *
8562 * <li> The expression used is as adopted in IERS Conventions (2003) and
8563 * comes from Souchay et al. (1999) after Simon et al. (1994).
8564 *</ol>
8565 *<p>References:
8566 *
8567 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8568 * IERS Technical Note No. 32, BKG (2004)
8569 *
8570 * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8571 * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8572 *
8573 * Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
8574 * Astron.Astrophys.Supp.Ser. 135, 111
8575 *
8576 *@version 2009 December 16
8577 *
8578 * @since Release 20101201
8579 *
8580 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8581 */
8582 public static double jauFave03(double t)
8583 {
8584 double a;
8585
8586
8587 /* Mean longitude of Venus (IERS Conventions 2003). */
8588 a = fmod(3.176146697 + 1021.3285546211 * t, D2PI);
8589
8590 return a;
8591
8592 }
8593
8594
8595 /**
8596 * Transform FK5 (J2000.0) star data into the Hipparcos system.
8597 *
8598 *<p>This function is derived from the International Astronomical Union's
8599 * SOFA (Standards Of Fundamental Astronomy) software collection.
8600 *
8601 *<p>Status: support function.
8602 *
8603 * Given (all FK5, equinox J2000.0, epoch J2000.0):
8604 * r5 double RA (radians)
8605 * d5 double Dec (radians)
8606 * dr5 double proper motion in RA (dRA/dt, rad/Jyear)
8607 * dd5 double proper motion in Dec (dDec/dt, rad/Jyear)
8608 * px5 double parallax (arcsec)
8609 * rv5 double radial velocity (km/s, positive = receding)
8610 *
8611 * Returned (all Hipparcos, epoch J2000.0):
8612 * rh double RA (radians)
8613 * dh double Dec (radians)
8614 * drh double proper motion in RA (dRA/dt, rad/Jyear)
8615 * ddh double proper motion in Dec (dDec/dt, rad/Jyear)
8616 * pxh double parallax (arcsec)
8617 * rvh double radial velocity (km/s, positive = receding)
8618 *
8619 * <p>Notes:
8620 * <ol>
8621 *
8622 * <li> This function transforms FK5 star positions and proper motions
8623 * into the system of the Hipparcos catalog.
8624 *
8625 * <li> The proper motions in RA are dRA/dt rather than
8626 * cos(Dec)*dRA/dt, and are per year rather than per century.
8627 *
8628 * <li> The FK5 to Hipparcos transformation is modeled as a pure
8629 * rotation and spin; zonal errors in the FK5 catalog are not
8630 * taken into account.
8631 *
8632 * <li> See also {@link #jauH2fk5}, {@link #jauFk5hz}, {@link #jauHfk5z}.
8633 *</ol>
8634 *<p>Called:<ul>
8635 * <li>{@link #jauStarpv} star catalog data to space motion pv-vector
8636 * <li>{@link #jauFk5hip} FK5 to Hipparcos rotation and spin
8637 * <li>{@link #jauRxp} product of r-matrix and p-vector
8638 * <li>{@link #jauPxp} vector product of two p-vectors
8639 * <li>{@link #jauPpp} p-vector plus p-vector
8640 * <li>{@link #jauPvstar} space motion pv-vector to star catalog data
8641 * </ul>
8642 *<p>Reference:
8643 *
8644 * <p>F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000).
8645 *
8646 *@version 2009 December 17
8647 *
8648 * @since Release 20101201
8649 *
8650 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8651 */
8652 public static CatalogCoords jauFk52h(double r5, double d5,
8653 double dr5, double dd5, double px5, double rv5)
8654 {
8655 int i;
8656 double pv5[][] = new double[2][3], r5h[][] = new double[3][3], s5h[] = new double[3], wxp[] = new double[3], vv[] = new double[3], pvh[][] = new double[2][3];
8657
8658
8659 /* FK5 barycentric position/velocity pv-vector (normalized). */
8660 jauStarpv(r5, d5, dr5, dd5, px5, rv5, pv5);
8661
8662 /* FK5 to Hipparcos orientation matrix and spin vector. */
8663 jauFk5hip(r5h, s5h);
8664
8665 /* Make spin units per day instead of per year. */
8666 for ( i = 0; i < 3; s5h[i++] /= 365.25 );
8667
8668 /* Orient the FK5 position into the Hipparcos system. */
8669 pvh[0] = jauRxp(r5h, pv5[0]);
8670
8671 /* Apply spin to the position giving an extra space motion component. */
8672 wxp = jauPxp(pv5[0],s5h);
8673
8674 /* Add this component to the FK5 space motion. */
8675 vv = jauPpp(wxp, pv5[1]);
8676
8677 /* Orient the FK5 space motion into the Hipparcos system. */
8678 pvh[1] = jauRxp(r5h, vv);
8679
8680 /* Hipparcos pv-vector to spherical. */
8681 CatalogCoords cat = null;
8682 try {
8683 cat = jauPvstar(pvh);
8684 } catch (JSOFAInternalError e) {
8685 //original code ignored possibility of error too...
8686 e.printStackTrace();
8687 }
8688
8689 return cat;
8690
8691 }
8692
8693
8694 /**
8695 * FK5 to Hipparcos rotation and spin.
8696 *
8697 *<p>This function is derived from the International Astronomical Union's
8698 * SOFA (Standards Of Fundamental Astronomy) software collection.
8699 *
8700 *<p>Status: support function.
8701 *
8702 *<!-- Returned: -->
8703 * @param r5h double[3][3] <u>returned</u> r-matrix: FK5 rotation wrt Hipparcos (Note 2)
8704 * @param s5h double[3] <u>returned</u> r-vector: FK5 spin wrt Hipparcos (Note 3)
8705 *
8706 * <p>Notes:
8707 * <ol>
8708 *
8709 * <li> This function models the FK5 to Hipparcos transformation as a
8710 * pure rotation and spin; zonal errors in the FK5 catalogue are
8711 * not taken into account.
8712 *
8713 * <li> The r-matrix r5h operates in the sense:
8714 *
8715 * P_Hipparcos = r5h x P_FK5
8716 *
8717 * where P_FK5 is a p-vector in the FK5 frame, and P_Hipparcos is
8718 * the equivalent Hipparcos p-vector.
8719 *
8720 * <li> The r-vector s5h represents the time derivative of the FK5 to
8721 * Hipparcos rotation. The units are radians per year (Julian,
8722 * TDB).
8723 *</ol>
8724 *<p>Called:<ul>
8725 * <li>{@link #jauRv2m} r-vector to r-matrix
8726 * </ul>
8727 *<p>Reference:
8728 *
8729 * <p>F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000).
8730 *
8731 *@version 2009 March 14
8732 *
8733 * @since Release 20101201
8734 *
8735 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8736 */
8737 public static void jauFk5hip(double r5h[][], double s5h[] )
8738 {
8739 double v[] = new double[3];
8740
8741 /* FK5 wrt Hipparcos orientation and spin (radians, radians/year) */
8742 double epx, epy, epz;
8743 double omx, omy, omz;
8744
8745
8746 epx = -19.9e-3 * DAS2R;
8747 epy = -9.1e-3 * DAS2R;
8748 epz = 22.9e-3 * DAS2R;
8749
8750 omx = -0.30e-3 * DAS2R;
8751 omy = 0.60e-3 * DAS2R;
8752 omz = 0.70e-3 * DAS2R;
8753
8754 /* FK5 to Hipparcos orientation expressed as an r-vector. */
8755 v[0] = epx;
8756 v[1] = epy;
8757 v[2] = epz;
8758
8759 /* Re-express as an r-matrix. */
8760 double[][] r5ht = jauRv2m(v);
8761 jauCr(r5ht, r5h);
8762
8763 /* Hipparcos wrt FK5 spin expressed as an r-vector. */
8764 s5h[0] = omx;
8765 s5h[1] = omy;
8766 s5h[2] = omz;
8767
8768 return;
8769
8770 }
8771
8772 /**
8773 * Position consisting of (α, δ) pairs in radians. Where α is right ascension (or longitude angle) and δ is declination (or latitude angle).
8774 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 1 Feb 2010
8775 *
8776 * @since AIDA Stage 1
8777 * @TODO needs better name cf {@link SphericalPosition}
8778 */
8779 public static class SphericalCoordinate {
8780 public double alpha;
8781 public double delta;
8782 public SphericalCoordinate(double alpha, double delta){
8783 this.alpha = alpha;
8784 this.delta = delta;
8785 }
8786 }
8787
8788 /**
8789 * Spherical coordinate with equation of origins .
8790 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 28 Mar 2014
8791 * @version $Revision$ $date$
8792 */
8793 public static class SphericalCoordinateEO {
8794 SphericalCoordinate pos;
8795 double eo;
8796 /**
8797 * @param pos
8798 * @param eo
8799 */
8800 public SphericalCoordinateEO(SphericalCoordinate pos, double eo) {
8801 this.pos = pos;
8802 this.eo = eo;
8803 }
8804
8805
8806 }
8807 /**
8808 * Transform an FK5 (J2000.0) star position into the system of the
8809 * Hipparcos catalogue, assuming zero Hipparcos proper motion.
8810 *
8811 *<p>This function is derived from the International Astronomical Union's
8812 * SOFA (Standards Of Fundamental Astronomy) software collection.
8813 *
8814 *<p>Status: support function.
8815 *
8816 *<!-- Given: -->
8817 * @param r5 double FK5 RA (radians), equinox J2000.0, at date
8818 * @param d5 double FK5 Dec (radians), equinox J2000.0, at date
8819 * @param date1 double TDB date (Notes 1,2)
8820 * @param date2 double TDB date (Notes 1,2)
8821 *
8822 *<!-- Returned: -->
8823 * @return rh double <u>returned</u> Hipparcos RA (radians)
8824 * dh double <u>returned</u> Hipparcos Dec (radians)
8825 *
8826 * <p>Notes:
8827 * <ol>
8828 *
8829 * <li> This function converts a star position from the FK5 system to
8830 * the Hipparcos system, in such a way that the Hipparcos proper
8831 * motion is zero. Because such a star has, in general, a non-zero
8832 * proper motion in the FK5 system, the function requires the date
8833 * at which the position in the FK5 system was determined.
8834 *
8835 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
8836 * convenient way between the two arguments. For example,
8837 * JD(TT)=2450123.7 could be expressed in any of these ways,
8838 * among others:
8839 *<pre>
8840 * date1 date2
8841 *
8842 * 2450123.7 0.0 (JD method)
8843 * 2451545.0 -1421.3 (J2000 method)
8844 * 2400000.5 50123.2 (MJD method)
8845 * 2450123.5 0.2 (date & time method)
8846 *</pre>
8847 * The JD method is the most natural and convenient to use in
8848 * cases where the loss of several decimal digits of resolution
8849 * is acceptable. The J2000 method is best matched to the way
8850 * the argument is handled internally and will deliver the
8851 * optimum resolution. The MJD method and the date & time methods
8852 * are both good compromises between resolution and convenience.
8853 *
8854 * <li> The FK5 to Hipparcos transformation is modeled as a pure
8855 * rotation and spin; zonal errors in the FK5 catalogue are not
8856 * taken into account.
8857 *
8858 * <li> The position returned by this function is in the Hipparcos
8859 * reference system but at date date1+date2.
8860 *
8861 * <li> See also jauFk52h, jauH2fk5, jauHfk5z.
8862 *</ol>
8863 *<p>Called:<ul>
8864 * <li>{@link #jauS2c} spherical coordinates to unit vector
8865 * <li>{@link #jauFk5hip} FK5 to Hipparcos rotation and spin
8866 * <li>{@link #jauSxp} multiply p-vector by scalar
8867 * <li>{@link #jauRv2m} r-vector to r-matrix
8868 * <li>{@link #jauTrxp} product of transpose of r-matrix and p-vector
8869 * <li>{@link #jauPxp} vector product of two p-vectors
8870 * <li>{@link #jauC2s} p-vector to spherical
8871 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
8872 * </ul>
8873 *<p>Reference:
8874 *
8875 * <p>F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739.
8876 *
8877 *@version 2009 December 17
8878 *
8879 * @since Release 20101201
8880 *
8881 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8882 */
8883 public static SphericalCoordinate jauFk5hz(double r5, double d5, double date1, double date2
8884 )
8885 {
8886 double t, p5e[] = new double[3], r5h[][] = new double[3][3], s5h[] = new double[3], vst[] = new double[3], rst[][] = new double[3][3], p5[] = new double[3],
8887 ph[] = new double[3];
8888
8889
8890 /* Interval from given date to fundamental epoch J2000.0 (JY). */
8891 t = - ((date1 - DJ00) + date2) / DJY;
8892
8893 /* FK5 barycentric position vector. */
8894 p5e = jauS2c(r5,d5);
8895
8896 /* FK5 to Hipparcos orientation matrix and spin vector. */
8897 jauFk5hip(r5h, s5h);
8898
8899 /* Accumulated Hipparcos wrt FK5 spin over that interval. */
8900 vst = jauSxp(t,s5h);
8901
8902 /* Express the accumulated spin as a rotation matrix. */
8903 rst = jauRv2m(vst);
8904
8905 /* Derotate the vector's FK5 axes back to date. */
8906 p5 = jauTrxp(rst, p5e);
8907
8908 /* Rotate the vector into the Hipparcos system. */
8909 ph = jauRxp(r5h, p5);
8910
8911 /* Hipparcos vector to spherical. */
8912 SphericalCoordinate sc = jauC2s(ph);
8913 double rh = jauAnp(sc.alpha);
8914 sc.alpha = rh;
8915
8916 return sc;
8917
8918 }
8919
8920
8921 /**
8922 * Form rotation matrix given the Fukushima-Williams angles.
8923 *
8924 *<p>This function is derived from the International Astronomical Union's
8925 * SOFA (Standards Of Fundamental Astronomy) software collection.
8926 *
8927 *<p>Status: support function.
8928 *
8929 *<!-- Given: -->
8930 * @param gamb double F-W angle gamma_bar (radians)
8931 * @param phib double F-W angle phi_bar (radians)
8932 * @param psi double F-W angle psi (radians)
8933 * @param eps double F-W angle epsilon (radians)
8934 *
8935 *<!-- Returned: -->
8936 * @return r double[3][3] <u>returned</u> rotation matrix
8937 *
8938 * <p>Notes:
8939 * <ol>
8940 *
8941 * <li> Naming the following points:
8942 *
8943 * e = J2000.0 ecliptic pole,
8944 * p = GCRS pole,
8945 * E = ecliptic pole of date,
8946 * and P = CIP,
8947 *
8948 * the four Fukushima-Williams angles are as follows:
8949 *
8950 * gamb = gamma = epE
8951 * phib = phi = pE
8952 * psi = psi = pEP
8953 * eps = epsilon = EP
8954 *
8955 * <li> The matrix representing the combined effects of frame bias,
8956 * precession and nutation is:
8957 *
8958 * NxPxB = R_1(-eps).R_3(-psi).R_1(phib).R_3(gamb)
8959 *
8960 * <li> Three different matrices can be constructed, depending on the
8961 * supplied angles:
8962 *
8963 * o To obtain the nutation x precession x frame bias matrix,
8964 * generate the four precession angles, generate the nutation
8965 * components and add them to the psi_bar and epsilon_A angles,
8966 * and call the present function.
8967 *
8968 * o To obtain the precession x frame bias matrix, generate the
8969 * four precession angles and call the present function.
8970 *
8971 * o To obtain the frame bias matrix, generate the four precession
8972 * angles for date J2000.0 and call the present function.
8973 *
8974 * The nutation-only and precession-only matrices can if necessary
8975 * be obtained by combining these three appropriately.
8976 *</ol>
8977 *<p>Called:<ul>
8978 * <li>{@link #jauIr} initialize r-matrix to identity
8979 * <li>{@link #jauRz} rotate around Z-axis
8980 * <li>{@link #jauRx} rotate around X-axis
8981 * </ul>
8982 *<p>Reference:
8983 *
8984 * Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
8985 *
8986 *@version 2009 December 17
8987 *
8988 * @since Release 20101201
8989 *
8990 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8991 */
8992 public static double[][] jauFw2m(double gamb, double phib, double psi, double eps)
8993 {
8994 /* Construct the matrix. */
8995 double r[][] = new double[3][3];
8996 jauIr(r);
8997 jauRz(gamb, r);
8998 jauRx(phib, r);
8999 jauRz(-psi, r);
9000 jauRx(-eps, r);
9001
9002 return r;
9003
9004 }
9005
9006
9007 /**
9008 * CIP X,Y given Fukushima-Williams bias-precession-nutation angles.
9009 *
9010 *<p>This function is derived from the International Astronomical Union's
9011 * SOFA (Standards Of Fundamental Astronomy) software collection.
9012 *
9013 *<p>Status: support function.
9014 *
9015 *<!-- Given: -->
9016 * @param gamb double F-W angle gamma_bar (radians)
9017 * @param phib double F-W angle phi_bar (radians)
9018 * @param psi double F-W angle psi (radians)
9019 * @param eps double F-W angle epsilon (radians)
9020 *
9021 *<!-- Returned: -->
9022 * @return CIP unit vector X,Y
9023 *
9024 * <p>Notes:
9025 * <ol>
9026 *
9027 * <li> Naming the following points:
9028 *
9029 * e = J2000.0 ecliptic pole,
9030 * p = GCRS pole
9031 * E = ecliptic pole of date,
9032 * and P = CIP,
9033 *
9034 * the four Fukushima-Williams angles are as follows:
9035 *
9036 * gamb = gamma = epE
9037 * phib = phi = pE
9038 * psi = psi = pEP
9039 * eps = epsilon = EP
9040 *
9041 * <li> The matrix representing the combined effects of frame bias,
9042 * precession and nutation is:
9043 *
9044 * NxPxB = R_1(-epsA).R_3(-psi).R_1(phib).R_3(gamb)
9045 *
9046 * The returned values x,y are elements [2][0] and [2][1] of the
9047 * matrix. Near J2000.0, they are essentially angles in radians
9048 *
9049 * X,Y are elements (3,1) and (3,2) of the matrix.
9050 *</ol>
9051 *<p>Called:<ul>
9052 * <li>{@link #jauFw2m} F-W angles to r-matrix
9053 * <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
9054 * </ul>
9055 *<p>Reference:
9056 *
9057 * Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
9058 *
9059 *@version 2009 December 17
9060 *
9061 * @since Release 20101201
9062 *
9063 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9064 */
9065 public static CelestialIntermediatePole jauFw2xy(double gamb, double phib, double psi, double eps)
9066 {
9067 double r[][] = new double[3][3];
9068
9069
9070 /* Form NxPxB matrix. */
9071 r = jauFw2m(gamb, phib, psi, eps);
9072
9073 /* Extract CIP X,Y. */
9074 return jauBpn2xy(r);
9075
9076 }
9077
9078 /**
9079 * Geodetic coordinates.
9080 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 4 Feb 2010
9081 *
9082 * @since AIDA Stage 1
9083 */
9084 public static class GeodeticCoord {
9085 /** longitude (radians, east +ve) */
9086 public double elong;
9087 /** latitude (geodetic, radians) */
9088 public double phi;
9089 /** height above ellipsoid (geodetic) */
9090 public double height;
9091 public GeodeticCoord(double elong, double phi, double height) {
9092 this.elong = elong;
9093 this.phi = phi;
9094 this.height = height;
9095 }
9096 }
9097 /**
9098 * Transform geocentric coordinates to geodetic using the specified
9099 * reference ellipsoid.
9100 *
9101 *<p>This function is derived from the International Astronomical Union's
9102 * JSOFA (Standards of Fundamental Astronomy) software collection.
9103 *
9104 *<p>Status: canonical transformation.
9105 *
9106 *<!-- Given: -->
9107 * @param n int ellipsoid identifier (Note 1)
9108 * @param xyz double[3] geocentric vector (Note 2)
9109 *
9110 *<!-- Returned: -->
9111 * @return elong double <u>returned</u> longitude (radians, east +ve)
9112 * phi double <u>returned</u> latitude (geodetic, radians, Note 3)
9113 * height double <u>returned</u> height above ellipsoid (geodetic, Notes 2,3)
9114 *
9115 * <!-- Returned (function value): -->
9116 * @throws JSOFAIllegalParameter
9117 * 0 = OK
9118 * -1 = illegal identifier (Note 3)
9119 * -2 = internal error (Note 3)
9120 *
9121 * <p>Notes:
9122 * <ol>
9123 *
9124 * <li> The identifier n is a number that specifies the choice of
9125 * reference ellipsoid. The following are supported:
9126 *
9127 * n ellipsoid
9128 *
9129 * 1 WGS84
9130 * 2 GRS80
9131 *
9132 * The number n has no significance outside the JSOFA software.
9133 *
9134 * <li> The geocentric vector (xyz, given) and height (height, returned)
9135 * are in meters.
9136 *
9137 * <li> An error status -1 means that the identifier n is illegal. An
9138 * error status -2 is theoretically impossible. In all error cases,
9139 * phi and height are both set to -1e9.
9140 *
9141 * <li> The inverse transformation is performed in the function jauGd2gc.
9142 *</ol>
9143 *<p>Called:<ul>
9144 * <li>{@link #jauEform} Earth reference ellipsoids
9145 * <li>{@link #jauGc2gde} geocentric to geodetic transformation, general
9146 * </ul>
9147 *@version 2010 January 18
9148 *
9149 * @since Release 20101201
9150 *
9151 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9152 */
9153 public static GeodeticCoord jauGc2gd ( int n, double xyz[] ) throws JSOFAIllegalParameter
9154 {
9155 GeodeticCoord gc;
9156
9157
9158 /* Obtain reference ellipsoid parameters. */
9159 ReferenceEllipsoid el = jauEform ( n );
9160
9161 /* If OK, transform x,y,z to longitude, geodetic latitude, height. */
9162 gc = jauGc2gde ( el.a, el.f, xyz);
9163
9164 /* Return the status. */
9165 return gc;
9166
9167
9168 }
9169
9170 /**
9171 * Transform geocentric coordinates to geodetic for a reference
9172 * ellipsoid of specified form.
9173 *
9174 *<p>This function is derived from the International Astronomical Union's
9175 * JSOFA (Standards of Fundamental Astronomy) software collection.
9176 *
9177 *<p>Status: support function.
9178 *
9179 *<!-- Given: -->
9180 * @param a double equatorial radius (Notes 2,4)
9181 * @param f double flattening (Note 3)
9182 * @param xyz double[3] geocentric vector (Note 4)
9183 *
9184 *<!-- Returned: -->
9185 * @return GeodeticCoord logitude (radians, east +ve) latitude (geodetic, radians) height above ellipsoid (geodetic, Note 4)
9186 *
9187 * @throws JSOFAIllegalParameter
9188 * int status:
9189 *
9190 * -1 = illegal a
9191 * -2 = illegal f
9192 *
9193 * <p>Notes:
9194 * <ol>
9195 *
9196 * <li> This function is based on the GCONV2H Fortran subroutine by
9197 * Toshio Fukushima (see reference).
9198 *
9199 * <li> The equatorial radius, a, can be in any units, but meters is
9200 * the conventional choice.
9201 *
9202 * <li> The flattening, f, is (for the Earth) a value around 0.00335,
9203 * i.e. around 1/298.
9204 *
9205 * <li> The equatorial radius, a, and the geocentric vector, xyz,
9206 * must be given in the same units, and determine the units of
9207 * the returned height, height.
9208 *
9209 * <li> If an error occurs (status < 0), elong, phi and height are
9210 * unchanged.
9211 *
9212 * <li> The inverse transformation is performed in the function
9213 * jauGd2gce.
9214 *
9215 * <li> The transformation for a standard ellipsoid (such as WGS84) can
9216 * more conveniently be performed by calling jauGc2gd, which uses a
9217 * numerical code (1 for WGS84) to identify the required A and F
9218 * values.
9219 *</ol>
9220 *<p>Reference:
9221 *
9222 * Fukushima, T., "Transformation from Cartesian to geodetic
9223 * coordinates accelerated by Halley's method", J.Geodesy (2006)
9224 * 79: 689-693
9225 *
9226 *@version 2009 November 2
9227 *
9228 * @since Release 20101201
9229 *
9230 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9231 *
9232 */
9233 public static GeodeticCoord jauGc2gde ( double a, double f, double xyz[] ) throws JSOFAIllegalParameter
9234 {
9235 double aeps2, e2, e4t, ec2, ec, b, x, y, z, p2, absz, p, s0, pn, zc,
9236 c0, c02, c03, s02, s03, a02, a0, a03, d0, f0, b0, s1,
9237 cc, s12, cc2;
9238
9239 double phi, height;
9240 /* ------------- */
9241 /* Preliminaries */
9242 /* ------------- */
9243
9244 /* Validate ellipsoid parameters. */
9245 if ( f < 0.0 || f >= 1.0 ) throw new JSOFAIllegalParameter("bad f", -1);
9246 if ( a <= 0.0 ) throw new JSOFAIllegalParameter("bad a", -2);
9247
9248 /* Functions of ellipsoid parameters (with further validation of f). */
9249 aeps2 = a*a * 1e-32;
9250 e2 = (2.0 - f) * f;
9251 e4t = e2*e2 * 1.5;
9252 ec2 = 1.0 - e2;
9253 if ( ec2 <= 0.0 ) throw new JSOFAIllegalParameter("bad f", -1);
9254 ec = sqrt(ec2);
9255 b = a * ec;
9256
9257 /* Cartesian components. */
9258 x = xyz[0];
9259 y = xyz[1];
9260 z = xyz[2];
9261
9262 /* Distance from polar axis squared. */
9263 p2 = x*x + y*y;
9264
9265 /* Longitude. */
9266 double elong = p2 > 0.0 ? atan2(y, x) : 0.0;
9267
9268 /* Unsigned z-coordinate. */
9269 absz = abs(z);
9270
9271 /* Proceed unless polar case. */
9272 if ( p2 > aeps2 ) {
9273
9274 /* Distance from polar axis. */
9275 p = sqrt(p2);
9276
9277 /* Normalization. */
9278 s0 = absz / a;
9279 pn = p / a;
9280 zc = ec * s0;
9281
9282 /* Prepare Newton correction factors. */
9283 c0 = ec * pn;
9284 c02 = c0 * c0;
9285 c03 = c02 * c0;
9286 s02 = s0 * s0;
9287 s03 = s02 * s0;
9288 a02 = c02 + s02;
9289 a0 = sqrt(a02);
9290 a03 = a02 * a0;
9291 d0 = zc*a03 + e2*s03;
9292 f0 = pn*a03 - e2*c03;
9293
9294 /* Prepare Halley correction factor. */
9295 b0 = e4t * s02 * c02 * pn * (a0 - ec);
9296 s1 = d0*f0 - b0*s0;
9297 cc = ec * (f0*f0 - b0*c0);
9298
9299 /* Evaluate latitude and height. */
9300 phi = atan(s1/cc);
9301 s12 = s1 * s1;
9302 cc2 = cc * cc;
9303 height = (p*cc + absz*s1 - a * sqrt(ec2*s12 + cc2)) /
9304 sqrt(s12 + cc2);
9305 } else {
9306
9307 /* Exception: pole. */
9308 phi = DPI / 2.0;
9309 height = absz - b;
9310 }
9311
9312 /* Restore sign of latitude. */
9313 if ( z < 0 ) phi = -phi;
9314
9315 /* OK status. */
9316 return new GeodeticCoord(elong, phi, height);
9317
9318
9319 }
9320
9321
9322 /**
9323 * Transform geodetic coordinates to geocentric using the specified
9324 * reference ellipsoid.
9325 *
9326 *<p>This function is derived from the International Astronomical Union's
9327 * JSOFA (Standards of Fundamental Astronomy) software collection.
9328 *
9329 *<p>Status: canonical transformation.
9330 *
9331 *<!-- Given: -->
9332 * @param n int ellipsoid identifier (Note 1)
9333 * @param elong double longitude (radians, east +ve)
9334 * @param phi double latitude (geodetic, radians, Note 3)
9335 * @param height double height above ellipsoid (geodetic, Notes 2,3)
9336 *
9337 *<!-- Returned: -->
9338 * @return xyz double[3] <u>returned</u> geocentric vector (Note 2)
9339 *
9340 * <!-- Returned (function value): -->
9341 * @throws JSOFAIllegalParameter
9342 * -1 = illegal identifier (Note 3)
9343 * -2 = illegal case (Note 3)
9344 *
9345 * <p>Notes:
9346 * <ol>
9347 *
9348 * <li> The identifier n is a number that specifies the choice of
9349 * reference ellipsoid. The following are supported:
9350 *
9351 * n ellipsoid
9352 *
9353 * 1 WGS84
9354 * 2 GRS80
9355 *
9356 * The number n has no significance outside the JSOFA software.
9357 *
9358 * <li> The height (height, given) and the geocentric vector (xyz,
9359 * returned) are in meters.
9360 *
9361 * <li> No validation is performed on the arguments elong, phi and
9362 * height. An error status -1 means that the identifier n is
9363 * illegal. An error status -2 protects against cases that would
9364 * lead to arithmetic exceptions. In all error cases, xyz is set
9365 * to zeros.
9366 *
9367 * <li> The inverse transformation is performed in the function jauGc2gd.
9368 *</ol>
9369 *<p>Called:<ul>
9370 * <li>{@link #jauEform} Earth reference ellipsoids
9371 * <li>{@link #jauGd2gce} geodetic to geocentric transformation, general
9372 * <li>{@link #jauZp} zero p-vector
9373 * </ul>
9374 *@version 2010 January 18
9375 *
9376 * @since Release 20101201
9377 *
9378 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9379 */
9380 public static double[] jauGd2gc ( int n, double elong, double phi, double height ) throws JSOFAIllegalParameter, JSOFAInternalError
9381 {
9382
9383
9384 /* Obtain reference ellipsoid parameters. */
9385 ReferenceEllipsoid em = jauEform ( n );
9386
9387 /* If OK, transform longitude, geodetic latitude, height to x,y,z. */
9388 return jauGd2gce ( em.a, em.f, elong, phi, height );
9389
9390
9391 }
9392
9393
9394 /**
9395 * Transform geodetic coordinates to geocentric for a reference
9396 * ellipsoid of specified form.
9397 *
9398 *<p>This function is derived from the International Astronomical Union's
9399 * JSOFA (Standards of Fundamental Astronomy) software collection.
9400 *
9401 *<p>Status: support function.
9402 *
9403 *<!-- Given: -->
9404 * @param a double equatorial radius (Notes 1,4)
9405 * @param f double flattening (Notes 2,4)
9406 * @param elong double longitude (radians, east +ve)
9407 * @param phi double latitude (geodetic, radians, Note 4)
9408 * @param height double height above ellipsoid (geodetic, Notes 3,4)
9409 *
9410 *<!-- Returned: -->
9411 * @return xyz double[3] <u>returned</u> geocentric vector (Note 3)
9412 *
9413 * <!-- Returned (function value): -->
9414 * @throws JSOFAInternalError
9415 * 0 = OK
9416 * -1 = illegal case (Note 4)
9417 * <p>Notes:
9418 * <ol>
9419 *
9420 * <li> The equatorial radius, a, can be in any units, but meters is
9421 * the conventional choice.
9422 *
9423 * <li> The flattening, f, is (for the Earth) a value around 0.00335,
9424 * i.e. around 1/298.
9425 *
9426 * <li> The equatorial radius, a, and the height, height, must be
9427 * given in the same units, and determine the units of the
9428 * returned geocentric vector, xyz.
9429 *
9430 * <li> No validation is performed on individual arguments. The error
9431 * status -1 protects against (unrealistic) cases that would lead
9432 * to arithmetic exceptions. If an error occurs, xyz is unchanged.
9433 *
9434 * <li> The inverse transformation is performed in the function
9435 * jauGc2gde.
9436 *
9437 * <li> The transformation for a standard ellipsoid (such as WGS84) can
9438 * more conveniently be performed by calling jauGd2gc, which uses a
9439 * numerical code (1 for WGS84) to identify the required a and f
9440 * values.
9441 *</ol>
9442 *<p>References:
9443 *
9444 * <p>Green, R.M., Spherical Astronomy, Cambridge University Press,
9445 * (1985) Section 4.5, p96.
9446 *
9447 * <p>Explanatory Supplement to the Astronomical Almanac,
9448 * P. Kenneth Seidelmann (ed), University Science Books (1992),
9449 * Section 4.22, p202.
9450 *
9451 *@version 2009 November 2
9452 *
9453 * @since Release 20101201
9454 *
9455 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9456 */
9457 public static double[] jauGd2gce ( double a, double f, double elong, double phi,
9458 double height ) throws JSOFAInternalError
9459 {
9460 double sp, cp, w, d, ac, as, r;
9461 double xyz[] = new double[3];
9462
9463
9464 /* Functions of geodetic latitude. */
9465 sp = sin(phi);
9466 cp = cos(phi);
9467 w = 1.0 - f;
9468 w = w * w;
9469 d = cp*cp + w*sp*sp;
9470 if ( d <= 0.0 ) throw new JSOFAInternalError("illegal combination of arguments d< 0", -1);
9471 ac = a / sqrt(d);
9472 as = w * ac;
9473
9474 /* Geocentric vector. */
9475 r = (ac + height) * cp;
9476 xyz[0] = r * cos(elong);
9477 xyz[1] = r * sin(elong);
9478 xyz[2] = (as + height) * sp;
9479
9480 /* Success. */
9481 return xyz;
9482
9483
9484 }
9485
9486
9487 /**
9488 * Greenwich mean sidereal time (model consistent with IAU 2000
9489 * resolutions).
9490 *
9491 *<p>This function is derived from the International Astronomical Union's
9492 * SOFA (Standards Of Fundamental Astronomy) software collection.
9493 *
9494 *<p>Status: canonical model.
9495 *
9496 *<!-- Given: -->
9497 * @param uta double UT1 as a 2-part Julian Date (Notes 1,2)
9498 * @param utb double UT1 as a 2-part Julian Date (Notes 1,2)
9499 * @param tta double TT as a 2-part Julian Date (Notes 1,2)
9500 * @param ttb double TT as a 2-part Julian Date (Notes 1,2)
9501 *
9502 * <!-- Returned (function value): -->
9503 * @return double Greenwich mean sidereal time (radians)
9504 *
9505 * <p>Notes:
9506 * <ol>
9507 *
9508 * <li> The UT1 and TT dates uta+utb and tta+ttb respectively, are both
9509 * Julian Dates, apportioned in any convenient way between the
9510 * argument pairs. For example, JD=2450123.7 could be expressed in
9511 * any of these ways, among others:
9512 *<pre>
9513 * Part A Part B
9514 *
9515 * 2450123.7 0.0 (JD method)
9516 * 2451545.0 -1421.3 (J2000 method)
9517 * 2400000.5 50123.2 (MJD method)
9518 * 2450123.5 0.2 (date & time method)
9519 *</pre>
9520 * The JD method is the most natural and convenient to use in
9521 * cases where the loss of several decimal digits of resolution
9522 * is acceptable (in the case of UT; the TT is not at all critical
9523 * in this respect). The J2000 and MJD methods are good compromises
9524 * between resolution and convenience. For UT, the date & time
9525 * method is best matched to the algorithm that is used by the Earth
9526 * Rotation Angle function, called internally: maximum precision is
9527 * delivered when the uta argument is for 0hrs UT1 on the day in
9528 * question and the utb argument lies in the range 0 to 1, or vice
9529 * versa.
9530 *
9531 * <li> Both UT1 and TT are required, UT1 to predict the Earth rotation
9532 * and TT to predict the effects of precession. If UT1 is used for
9533 * both purposes, errors of order 100 microarcseconds result.
9534 *
9535 * <li> This GMST is compatible with the IAU 2000 resolutions and must be
9536 * used only in conjunction with other IAU 2000 compatible
9537 * components such as precession-nutation and equation of the
9538 * equinoxes.
9539 *
9540 * <li> The result is returned in the range 0 to 2pi.
9541 *
9542 * <li> The algorithm is from Capitaine et al. (2003) and IERS
9543 * Conventions 2003.
9544 *</ol>
9545 *<p>Called:<ul>
9546 * <li>{@link #jauEra00} Earth rotation angle, IAU 2000
9547 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
9548 * </ul>
9549 *<p>References:
9550 *
9551 * <p>Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
9552 * implement the IAU 2000 definition of UT1", Astronomy &
9553 * Astrophysics, 406, 1135-1149 (2003)
9554 *
9555 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
9556 * IERS Technical Note No. 32, BKG (2004)
9557 *
9558 *@version 2009 March 16
9559 *
9560 * @since Release 20101201
9561 *
9562 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9563 */
9564 public static double jauGmst00(double uta, double utb, double tta, double ttb)
9565 {
9566 double t, gmst;
9567
9568
9569 /* TT Julian centuries since J2000.0. */
9570 t = ((tta - DJ00) + ttb) / DJC;
9571
9572 /* Greenwich Mean Sidereal Time, IAU 2000. */
9573 gmst = jauAnp(jauEra00(uta, utb) +
9574 ( 0.014506 +
9575 ( 4612.15739966 +
9576 ( 1.39667721 +
9577 ( -0.00009344 +
9578 ( 0.00001882 )
9579 * t) * t) * t) * t) * DAS2R);
9580
9581 return gmst;
9582
9583 }
9584
9585
9586 /**
9587 * Greenwich mean sidereal time (consistent with IAU 2006 precession).
9588 *
9589 *<p>This function is derived from the International Astronomical Union's
9590 * SOFA (Standards Of Fundamental Astronomy) software collection.
9591 *
9592 *<p>Status: canonical model.
9593 *
9594 *<!-- Given: -->
9595 * @param uta double UT1 as a 2-part Julian Date (Notes 1,2)
9596 * @param utb double UT1 as a 2-part Julian Date (Notes 1,2)
9597 * @param tta double TT as a 2-part Julian Date (Notes 1,2)
9598 * @param ttb double TT as a 2-part Julian Date (Notes 1,2)
9599 *
9600 * <!-- Returned (function value): -->
9601 * @return double Greenwich mean sidereal time (radians)
9602 *
9603 * <p>Notes:
9604 * <ol>
9605 *
9606 * <li> The UT1 and TT dates uta+utb and tta+ttb respectively, are both
9607 * Julian Dates, apportioned in any convenient way between the
9608 * argument pairs. For example, JD=2450123.7 could be expressed in
9609 * any of these ways, among others:
9610 *<pre>
9611 * Part A Part B
9612 *
9613 * 2450123.7 0.0 (JD method)
9614 * 2451545.0 -1421.3 (J2000 method)
9615 * 2400000.5 50123.2 (MJD method)
9616 * 2450123.5 0.2 (date & time method)
9617 *</pre>
9618 * The JD method is the most natural and convenient to use in
9619 * cases where the loss of several decimal digits of resolution
9620 * is acceptable (in the case of UT; the TT is not at all critical
9621 * in this respect). The J2000 and MJD methods are good compromises
9622 * between resolution and convenience. For UT, the date & time
9623 * method is best matched to the algorithm that is used by the Earth
9624 * rotation angle function, called internally: maximum precision is
9625 * delivered when the uta argument is for 0hrs UT1 on the day in
9626 * question and the utb argument lies in the range 0 to 1, or vice
9627 * versa.
9628 *
9629 * <li> Both UT1 and TT are required, UT1 to predict the Earth rotation
9630 * and TT to predict the effects of precession. If UT1 is used for
9631 * both purposes, errors of order 100 microarcseconds result.
9632 *
9633 * <li> This GMST is compatible with the IAU 2006 precession and must not
9634 * be used with other precession models.
9635 *
9636 * <li> The result is returned in the range 0 to 2pi.
9637 *</ol>
9638 *<p>Called:<ul>
9639 * <li>{@link #jauEra00} Earth rotation angle, IAU 2000
9640 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
9641 * </ul>
9642 *<p>Reference:
9643 *
9644 * <p>Capitaine, N., Wallace, P.T. & Chapront, J., 2005,
9645 * Astron.Astrophys. 432, 355
9646 *
9647 *@version 2008 May 24
9648 *
9649 * @since Release 20101201
9650 *
9651 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9652 */
9653 public static double jauGmst06(double uta, double utb, double tta, double ttb)
9654 {
9655 double t, gmst;
9656
9657
9658 /* TT Julian centuries since J2000.0. */
9659 t = ((tta - DJ00) + ttb) / DJC;
9660
9661 /* Greenwich mean sidereal time, IAU 2006. */
9662 gmst = jauAnp(jauEra00(uta, utb) +
9663 ( 0.014506 +
9664 ( 4612.156534 +
9665 ( 1.3915817 +
9666 ( -0.00000044 +
9667 ( -0.000029956 +
9668 ( -0.0000000368 )
9669 * t) * t) * t) * t) * t) * DAS2R);
9670
9671 return gmst;
9672
9673 }
9674
9675
9676 /**
9677 * Universal Time to Greenwich mean sidereal time (IAU 1982 model).
9678 *
9679 *<p>This function is derived from the International Astronomical Union's
9680 * SOFA (Standards Of Fundamental Astronomy) software collection.
9681 *
9682 *<p>Status: canonical model.
9683 *
9684 *<!-- Given: -->
9685 * @param dj1 double UT1 Julian Date (see note)
9686 * @param dj2 double UT1 Julian Date (see note)
9687 *
9688 * <!-- Returned (function value): -->
9689 * @return double Greenwich mean sidereal time (radians)
9690 *
9691 * <p>Notes:
9692 * <ol>
9693 *
9694 * <li> The UT1 date dj1+dj2 is a Julian Date, apportioned in any
9695 * convenient way between the arguments dj1 and dj2. For example,
9696 * JD(UT1)=2450123.7 could be expressed in any of these ways,
9697 * among others:
9698 *<pre>
9699 * dj1 dj2
9700 *
9701 * 2450123.7D0 0D0 (JD method)
9702 * 2451545D0 -1421.3D0 (J2000 method)
9703 * 2400000.5D0 50123.2D0 (MJD method)
9704 * 2450123.5D0 0.2D0 (date & time method)
9705 *</pre>
9706 * The JD method is the most natural and convenient to use in
9707 * cases where the loss of several decimal digits of resolution
9708 * is acceptable. The J2000 and MJD methods are good compromises
9709 * between resolution and convenience. The date & time method is
9710 * best matched to the algorithm used: maximum accuracy (or, at
9711 * least, minimum noise) is delivered when the dj1 argument is for
9712 * 0hrs UT1 on the day in question and the dj2 argument lies in the
9713 * range 0 to 1, or vice versa.
9714 *
9715 * <li> The algorithm is based on the IAU 1982 expression. This is
9716 * always described as giving the GMST at 0 hours UT1. In fact, it
9717 * gives the difference between the GMST and the UT, the steady
9718 * 4-minutes-per-day drawing-ahead of ST with respect to UT. When
9719 * whole days are ignored, the expression happens to equal the GMST
9720 * at 0 hours UT1 each day.
9721 *
9722 * <li> In this function, the entire UT1 (the sum of the two arguments
9723 * dj1 and dj2) is used directly as the argument for the standard
9724 * formula, the constant term of which is adjusted by 12 hours to
9725 * take account of the noon phasing of Julian Date. The UT1 is then
9726 * added, but omitting whole days to conserve accuracy.
9727 *</ol>
9728 *<p>Called:<ul>
9729 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
9730 * </ul>
9731 *<p>References:
9732 *
9733 * <p>Transactions of the International Astronomical Union,
9734 * XVIII B, 67 (1983).
9735 *
9736 * <p>Aoki et al., Astron. Astrophys. 105, 359-361 (1982).
9737 *
9738 *@version 2008 May 24
9739 *
9740 * @since Release 20101201
9741 *
9742 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9743 */
9744 public static double jauGmst82(double dj1, double dj2)
9745 {
9746 /* Coefficients of IAU 1982 GMST-UT1 model */
9747 double A = 24110.54841 - DAYSEC / 2.0;
9748 double B = 8640184.812866;
9749 double C = 0.093104;
9750 double D = -6.2e-6;
9751
9752 /* Note: the first constant, A, has to be adjusted by 12 hours */
9753 /* because the UT1 is supplied as a Julian date, which begins */
9754 /* at noon. */
9755
9756 double d1, d2, t, f, gmst;
9757
9758
9759 /* Julian centuries since fundamental epoch. */
9760 if (dj1 < dj2) {
9761 d1 = dj1;
9762 d2 = dj2;
9763 } else {
9764 d1 = dj2;
9765 d2 = dj1;
9766 }
9767 t = (d1 + (d2 - DJ00)) / DJC;
9768
9769 /* Fractional part of JD(UT1), in seconds. */
9770 f = DAYSEC * (fmod(d1, 1.0) + fmod(d2, 1.0));
9771
9772 /* GMST at this UT1. */
9773 gmst = jauAnp(DS2R * ((A + (B + (C + D * t) * t) * t) + f));
9774
9775 return gmst;
9776
9777 }
9778
9779
9780 /**
9781 * Greenwich apparent sidereal time (consistent with IAU 2000
9782 * resolutions).
9783 *
9784 *<p>This function is derived from the International Astronomical Union's
9785 * SOFA (Standards Of Fundamental Astronomy) software collection.
9786 *
9787 *<p>Status: canonical model.
9788 *
9789 *<!-- Given: -->
9790 * @param uta double UT1 as a 2-part Julian Date (Notes 1,2)
9791 * @param utb double UT1 as a 2-part Julian Date (Notes 1,2)
9792 * @param tta double TT as a 2-part Julian Date (Notes 1,2)
9793 * @param ttb double TT as a 2-part Julian Date (Notes 1,2)
9794 *
9795 * <!-- Returned (function value): -->
9796 * @return double Greenwich apparent sidereal time (radians)
9797 *
9798 * <p>Notes:
9799 * <ol>
9800 *
9801 * <li> The UT1 and TT dates uta+utb and tta+ttb respectively, are both
9802 * Julian Dates, apportioned in any convenient way between the
9803 * argument pairs. For example, JD=2450123.7 could be expressed in
9804 * any of these ways, among others:
9805 *<pre>
9806 * Part A Part B
9807 *
9808 * 2450123.7 0.0 (JD method)
9809 * 2451545.0 -1421.3 (J2000 method)
9810 * 2400000.5 50123.2 (MJD method)
9811 * 2450123.5 0.2 (date & time method)
9812 *</pre>
9813 * The JD method is the most natural and convenient to use in
9814 * cases where the loss of several decimal digits of resolution
9815 * is acceptable (in the case of UT; the TT is not at all critical
9816 * in this respect). The J2000 and MJD methods are good compromises
9817 * between resolution and convenience. For UT, the date & time
9818 * method is best matched to the algorithm that is used by the Earth
9819 * Rotation Angle function, called internally: maximum precision is
9820 * delivered when the uta argument is for 0hrs UT1 on the day in
9821 * question and the utb argument lies in the range 0 to 1, or vice
9822 * versa.
9823 *
9824 * <li> Both UT1 and TT are required, UT1 to predict the Earth rotation
9825 * and TT to predict the effects of precession-nutation. If UT1 is
9826 * used for both purposes, errors of order 100 microarcseconds
9827 * result.
9828 *
9829 * <li> This GAST is compatible with the IAU 2000 resolutions and must be
9830 * used only in conjunction with other IAU 2000 compatible
9831 * components such as precession-nutation.
9832 *
9833 * <li> The result is returned in the range 0 to 2pi.
9834 *
9835 * <li> The algorithm is from Capitaine et al. (2003) and IERS
9836 * Conventions 2003.
9837 *</ol>
9838 *<p>Called:<ul>
9839 * <li>{@link #jauGmst00} Greenwich mean sidereal time, IAU 2000
9840 * <li>{@link #jauEe00a} equation of the equinoxes, IAU 2000A
9841 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
9842 * </ul>
9843 *<p>References:
9844 *
9845 * <p>Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
9846 * implement the IAU 2000 definition of UT1", Astronomy &
9847 * Astrophysics, 406, 1135-1149 (2003)
9848 *
9849 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
9850 * IERS Technical Note No. 32, BKG (2004)
9851 *
9852 *@version 2008 May 16
9853 *
9854 * @since Release 20101201
9855 *
9856 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9857 */
9858 public static double jauGst00a(double uta, double utb, double tta, double ttb)
9859 {
9860 double gmst00, ee00a, gst;
9861
9862
9863 gmst00 = jauGmst00(uta, utb, tta, ttb);
9864 ee00a = jauEe00a(tta, ttb);
9865 gst = jauAnp(gmst00 + ee00a);
9866
9867 return gst;
9868
9869 }
9870
9871
9872 /**
9873 * Greenwich apparent sidereal time (consistent with IAU 2000
9874 * resolutions but using the truncated nutation model IAU 2000B).
9875 *
9876 *<p>This function is derived from the International Astronomical Union's
9877 * SOFA (Standards Of Fundamental Astronomy) software collection.
9878 *
9879 *<p>Status: support function.
9880 *
9881 *<!-- Given: -->
9882 * @param uta double UT1 as a 2-part Julian Date (Notes 1,2)
9883 * @param utb double UT1 as a 2-part Julian Date (Notes 1,2)
9884 *
9885 * <!-- Returned (function value): -->
9886 * @return double Greenwich apparent sidereal time (radians)
9887 *
9888 * <p>Notes:
9889 * <ol>
9890 *
9891 * <li> The UT1 date uta+utb is a Julian Date, apportioned in any
9892 * convenient way between the argument pair. For example,
9893 * JD=2450123.7 could be expressed in any of these ways, among
9894 * others:
9895 *<pre>
9896 * uta utb
9897 *
9898 * 2450123.7 0.0 (JD method)
9899 * 2451545.0 -1421.3 (J2000 method)
9900 * 2400000.5 50123.2 (MJD method)
9901 * 2450123.5 0.2 (date & time method)
9902 *</pre>
9903 * The JD method is the most natural and convenient to use in cases
9904 * where the loss of several decimal digits of resolution is
9905 * acceptable. The J2000 and MJD methods are good compromises
9906 * between resolution and convenience. For UT, the date & time
9907 * method is best matched to the algorithm that is used by the Earth
9908 * Rotation Angle function, called internally: maximum precision is
9909 * delivered when the uta argument is for 0hrs UT1 on the day in
9910 * question and the utb argument lies in the range 0 to 1, or vice
9911 * versa.
9912 *
9913 * <li> The result is compatible with the IAU 2000 resolutions, except
9914 * that accuracy has been compromised for the sake of speed and
9915 * convenience in two respects:
9916 *
9917 * . UT is used instead of TDB (or TT) to compute the precession
9918 * component of GMST and the equation of the equinoxes. This
9919 * results in errors of order 0.1 mas at present.
9920 *
9921 * . The IAU 2000B abridged nutation model (McCarthy & Luzum, 2001)
9922 * is used, introducing errors of up to 1 mas.
9923 *
9924 * <li> This GAST is compatible with the IAU 2000 resolutions and must be
9925 * used only in conjunction with other IAU 2000 compatible
9926 * components such as precession-nutation.
9927 *
9928 * <li> The result is returned in the range 0 to 2pi.
9929 *
9930 * <li> The algorithm is from Capitaine et al. (2003) and IERS
9931 * Conventions 2003.
9932 *</ol>
9933 *<p>Called:<ul>
9934 * <li>{@link #jauGmst00} Greenwich mean sidereal time, IAU 2000
9935 * <li>{@link #jauEe00b} equation of the equinoxes, IAU 2000B
9936 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
9937 * </ul>
9938 *<p>References:
9939 *
9940 * <p>Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
9941 * implement the IAU 2000 definition of UT1", Astronomy &
9942 * Astrophysics, 406, 1135-1149 (2003)
9943 *
9944 * <p>McCarthy, D.D. & Luzum, B.J., "An abridged model of the
9945 * precession-nutation of the celestial pole", Celestial Mechanics &
9946 * Dynamical Astronomy, 85, 37-49 (2003)
9947 *
9948 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
9949 * IERS Technical Note No. 32, BKG (2004)
9950 *
9951 *@version 2008 May 16
9952 *
9953 * @since Release 20101201
9954 *
9955 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9956 */
9957 public static double jauGst00b(double uta, double utb)
9958 {
9959 double gmst00, ee00b, gst;
9960
9961
9962 gmst00 = jauGmst00(uta, utb, uta, utb);
9963 ee00b = jauEe00b(uta, utb);
9964 gst = jauAnp(gmst00 + ee00b);
9965
9966 return gst;
9967
9968 }
9969
9970
9971 /**
9972 * Greenwich apparent sidereal time, IAU 2006, given the NPB matrix.
9973 *
9974 *<p>This function is derived from the International Astronomical Union's
9975 * SOFA (Standards Of Fundamental Astronomy) software collection.
9976 *
9977 *<p>Status: support function.
9978 *
9979 *<!-- Given: -->
9980 * @param uta double UT1 as a 2-part Julian Date (Notes 1,2)
9981 * @param utb double UT1 as a 2-part Julian Date (Notes 1,2)
9982 * @param tta double TT as a 2-part Julian Date (Notes 1,2)
9983 * @param ttb double TT as a 2-part Julian Date (Notes 1,2)
9984 * @param rnpb double[3][3] nutation x precession x bias matrix
9985 *
9986 * <!-- Returned (function value): -->
9987 * @return double Greenwich apparent sidereal time (radians)
9988 *
9989 * <p>Notes:
9990 * <ol>
9991 *
9992 * <li> The UT1 and TT dates uta+utb and tta+ttb respectively, are both
9993 * Julian Dates, apportioned in any convenient way between the
9994 * argument pairs. For example, JD=2450123.7 could be expressed in
9995 * any of these ways, among others:
9996 *<pre>
9997 * Part A Part B
9998 *
9999 * 2450123.7 0.0 (JD method)
10000 * 2451545.0 -1421.3 (J2000 method)
10001 * 2400000.5 50123.2 (MJD method)
10002 * 2450123.5 0.2 (date & time method)
10003 *</pre>
10004 * The JD method is the most natural and convenient to use in
10005 * cases where the loss of several decimal digits of resolution
10006 * is acceptable (in the case of UT; the TT is not at all critical
10007 * in this respect). The J2000 and MJD methods are good compromises
10008 * between resolution and convenience. For UT, the date & time
10009 * method is best matched to the algorithm that is used by the Earth
10010 * rotation angle function, called internally: maximum precision is
10011 * delivered when the uta argument is for 0hrs UT1 on the day in
10012 * question and the utb argument lies in the range 0 to 1, or vice
10013 * versa.
10014 *
10015 * <li> Both UT1 and TT are required, UT1 to predict the Earth rotation
10016 * and TT to predict the effects of precession-nutation. If UT1 is
10017 * used for both purposes, errors of order 100 microarcseconds
10018 * result.
10019 *
10020 * <li> Although the function uses the IAU 2006 series for s+XY/2, it is
10021 * otherwise independent of the precession-nutation model and can in
10022 * practice be used with any equinox-based NPB matrix.
10023 *
10024 * <li> The result is returned in the range 0 to 2pi.
10025 *</ol>
10026 *<p>Called:<ul>
10027 * <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
10028 * <li>{@link #jauS06} the CIO locator s, given X,Y, IAU 2006
10029 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
10030 * <li>{@link #jauEra00} Earth rotation angle, IAU 2000
10031 * <li>{@link #jauEors} equation of the origins, given NPB matrix and s
10032 * </ul>
10033 *<p>Reference:
10034 *
10035 * <p>Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
10036 *
10037 *@version 2008 May 24
10038 *
10039 * @since Release 20101201
10040 *
10041 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10042 */
10043 public static double jauGst06(double uta, double utb, double tta, double ttb,
10044 double rnpb[][])
10045 {
10046 double s, era, eors, gst;
10047
10048
10049 /* Extract CIP coordinates. */
10050 CelestialIntermediatePole cip = jauBpn2xy(rnpb);
10051
10052 /* The CIO locator, s. */
10053 s = jauS06(tta, ttb, cip.x, cip.y);
10054
10055 /* Greenwich apparent sidereal time. */
10056 era = jauEra00(uta, utb);
10057 eors = jauEors(rnpb, s);
10058 gst = jauAnp(era - eors);
10059
10060 return gst;
10061
10062 }
10063
10064
10065 /**
10066 * Greenwich apparent sidereal time (consistent with IAU 2000 and 2006
10067 * resolutions).
10068 *
10069 *<p>This function is derived from the International Astronomical Union's
10070 * SOFA (Standards Of Fundamental Astronomy) software collection.
10071 *
10072 *<p>Status: canonical model.
10073 *
10074 *<!-- Given: -->
10075 * @param uta double UT1 as a 2-part Julian Date (Notes 1,2)
10076 * @param utb double UT1 as a 2-part Julian Date (Notes 1,2)
10077 * @param tta double TT as a 2-part Julian Date (Notes 1,2)
10078 * @param ttb double TT as a 2-part Julian Date (Notes 1,2)
10079 *
10080 * <!-- Returned (function value): -->
10081 * @return double Greenwich apparent sidereal time (radians)
10082 *
10083 * <p>Notes:
10084 * <ol>
10085 *
10086 * <li> The UT1 and TT dates uta+utb and tta+ttb respectively, are both
10087 * Julian Dates, apportioned in any convenient way between the
10088 * argument pairs. For example, JD=2450123.7 could be expressed in
10089 * any of these ways, among others:
10090 *<pre>
10091 * Part A Part B
10092 *
10093 * 2450123.7 0.0 (JD method)
10094 * 2451545.0 -1421.3 (J2000 method)
10095 * 2400000.5 50123.2 (MJD method)
10096 * 2450123.5 0.2 (date & time method)
10097 *</pre>
10098 * The JD method is the most natural and convenient to use in
10099 * cases where the loss of several decimal digits of resolution
10100 * is acceptable (in the case of UT; the TT is not at all critical
10101 * in this respect). The J2000 and MJD methods are good compromises
10102 * between resolution and convenience. For UT, the date & time
10103 * method is best matched to the algorithm that is used by the Earth
10104 * rotation angle function, called internally: maximum precision is
10105 * delivered when the uta argument is for 0hrs UT1 on the day in
10106 * question and the utb argument lies in the range 0 to 1, or vice
10107 * versa.
10108 *
10109 * <li> Both UT1 and TT are required, UT1 to predict the Earth rotation
10110 * and TT to predict the effects of precession-nutation. If UT1 is
10111 * used for both purposes, errors of order 100 microarcseconds
10112 * result.
10113 *
10114 * <li> This GAST is compatible with the IAU 2000/2006 resolutions and
10115 * must be used only in conjunction with IAU 2006 precession and
10116 * IAU 2000A nutation.
10117 *
10118 * <li> The result is returned in the range 0 to 2pi.
10119 *</ol>
10120 *<p>Called:<ul>
10121 * <li>{@link #jauPnm06a} classical NPB matrix, IAU 2006/2000A
10122 * <li>{@link #jauGst06} Greenwich apparent ST, IAU 2006, given NPB matrix
10123 * </ul>
10124 *<p>Reference:
10125 *
10126 * <p>Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
10127 *
10128 *@version 2008 May 16
10129 *
10130 * @since Release 20101201
10131 *
10132 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10133 */
10134 public static double jauGst06a(double uta, double utb, double tta, double ttb)
10135 {
10136 double rnpb[][] = new double[3][3], gst;
10137
10138
10139 /* Classical nutation x precession x bias matrix, IAU 2000A. */
10140 rnpb = jauPnm06a(tta, ttb);
10141
10142 /* Greenwich apparent sidereal time. */
10143 gst = jauGst06(uta, utb, tta, ttb, rnpb);
10144
10145 return gst;
10146
10147 }
10148
10149
10150 /**
10151 * Greenwich apparent sidereal time (consistent with IAU 1982/94
10152 * resolutions).
10153 *
10154 *<p>This function is derived from the International Astronomical Union's
10155 * SOFA (Standards Of Fundamental Astronomy) software collection.
10156 *
10157 *<p>Status: support function.
10158 *
10159 *<!-- Given: -->
10160 * @param uta double UT1 as a 2-part Julian Date (Notes 1,2)
10161 * @param utb double UT1 as a 2-part Julian Date (Notes 1,2)
10162 *
10163 * <!-- Returned (function value): -->
10164 * @return double Greenwich apparent sidereal time (radians)
10165 *
10166 * <p>Notes:
10167 * <ol>
10168 *
10169 * <li> The UT1 date uta+utb is a Julian Date, apportioned in any
10170 * convenient way between the argument pair. For example,
10171 * JD=2450123.7 could be expressed in any of these ways, among
10172 * others:
10173 *<pre>
10174 * uta utb
10175 *
10176 * 2450123.7 0.0 (JD method)
10177 * 2451545.0 -1421.3 (J2000 method)
10178 * 2400000.5 50123.2 (MJD method)
10179 * 2450123.5 0.2 (date & time method)
10180 *</pre>
10181 * The JD method is the most natural and convenient to use in cases
10182 * where the loss of several decimal digits of resolution is
10183 * acceptable. The J2000 and MJD methods are good compromises
10184 * between resolution and convenience. For UT, the date & time
10185 * method is best matched to the algorithm that is used by the Earth
10186 * Rotation Angle function, called internally: maximum precision is
10187 * delivered when the uta argument is for 0hrs UT1 on the day in
10188 * question and the utb argument lies in the range 0 to 1, or vice
10189 * versa.
10190 *
10191 * <li> The result is compatible with the IAU 1982 and 1994 resolutions,
10192 * except that accuracy has been compromised for the sake of
10193 * convenience in that UT is used instead of TDB (or TT) to compute
10194 * the equation of the equinoxes.
10195 *
10196 * <li> This GAST must be used only in conjunction with contemporaneous
10197 * IAU standards such as 1976 precession, 1980 obliquity and 1982
10198 * nutation. It is not compatible with the IAU 2000 resolutions.
10199 *
10200 * <li> The result is returned in the range 0 to 2pi.
10201 *</ol>
10202 *<p>Called:<ul>
10203 * <li>{@link #jauGmst82} Greenwich mean sidereal time, IAU 1982
10204 * <li>{@link #jauEqeq94} equation of the equinoxes, IAU 1994
10205 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
10206 * </ul>
10207 *<p>References:
10208 *
10209 * <p>Explanatory Supplement to the Astronomical Almanac,
10210 * P. Kenneth Seidelmann (ed), University Science Books (1992)
10211 *
10212 * IAU Resolution C7, Recommendation 3 (1994)
10213 *
10214 *@version 2008 May 16
10215 *
10216 * @since Release 20101201
10217 *
10218 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10219 */
10220 public static double jauGst94(double uta, double utb)
10221 {
10222 double gmst82, eqeq94, gst;
10223
10224
10225 gmst82 = jauGmst82(uta, utb);
10226 eqeq94 = jauEqeq94(uta, utb);
10227 gst = jauAnp(gmst82 + eqeq94);
10228
10229 return gst;
10230
10231 }
10232
10233
10234 /**
10235 * Transform Hipparcos star data into the FK5 (J2000.0) system.
10236 *
10237 *<p>This function is derived from the International Astronomical Union's
10238 * SOFA (Standards Of Fundamental Astronomy) software collection.
10239 *
10240 *<p>Status: support function.
10241 *
10242 * Given (all Hipparcos, epoch J2000.0):
10243 * rh double RA (radians)
10244 * dh double Dec (radians)
10245 * drh double proper motion in RA (dRA/dt, rad/Jyear)
10246 * ddh double proper motion in Dec (dDec/dt, rad/Jyear)
10247 * pxh double parallax (arcsec)
10248 * rvh double radial velocity (km/s, positive = receding)
10249 *
10250 * Returned (all FK5, equinox J2000.0, epoch J2000.0):
10251 * r5 double RA (radians)
10252 * d5 double Dec (radians)
10253 * dr5 double proper motion in RA (dRA/dt, rad/Jyear)
10254 * dd5 double proper motion in Dec (dDec/dt, rad/Jyear)
10255 * px5 double parallax (arcsec)
10256 * rv5 double radial velocity (km/s, positive = receding)
10257 *
10258 * <p>Notes:
10259 * <ol>
10260 *
10261 * <li> This function transforms Hipparcos star positions and proper
10262 * motions into FK5 J2000.0.
10263 *
10264 * <li> The proper motions in RA are dRA/dt rather than
10265 * cos(Dec)*dRA/dt, and are per year rather than per century.
10266 *
10267 * <li> The FK5 to Hipparcos transformation is modeled as a pure
10268 * rotation and spin; zonal errors in the FK5 catalog are not
10269 * taken into account.
10270 *
10271 * <li> See also jauFk52h, jauFk5hz, jauHfk5z.
10272 *</ol>
10273 *<p>Called:<ul>
10274 * <li>{@link #jauStarpv} star catalog data to space motion pv-vector
10275 * <li>{@link #jauFk5hip} FK5 to Hipparcos rotation and spin
10276 * <li>{@link #jauRv2m} r-vector to r-matrix
10277 * <li>{@link #jauRxp} product of r-matrix and p-vector
10278 * <li>{@link #jauTrxp} product of transpose of r-matrix and p-vector
10279 * <li>{@link #jauPxp} vector product of two p-vectors
10280 * <li>{@link #jauPmp} p-vector minus p-vector
10281 * <li>{@link #jauPvstar} space motion pv-vector to star catalog data
10282 * </ul>
10283 *<p>Reference:
10284 *
10285 * <p>F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000).
10286 *
10287 *@version 2009 December 17
10288 *
10289 * @since Release 20101201
10290 *
10291 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10292 */
10293 public static CatalogCoords jauH2fk5(double rh, double dh,
10294 double drh, double ddh, double pxh, double rvh)
10295 {
10296 int i;
10297 double pvh[][] = new double[2][3], r5h[][] = new double[3][3], s5h[] = new double[3], sh[] = new double[3], wxp[] = new double[3], vv[] = new double[3], pv5[][] = new double[2][3];
10298
10299
10300 /* Hipparcos barycentric position/velocity pv-vector (normalized). */
10301 jauStarpv(rh, dh, drh, ddh, pxh, rvh, pvh);
10302
10303 /* FK5 to Hipparcos orientation matrix and spin vector. */
10304 jauFk5hip(r5h, s5h);
10305
10306 /* Make spin units per day instead of per year. */
10307 for ( i = 0; i < 3; s5h[i++] /= 365.25 );
10308
10309 /* Orient the spin into the Hipparcos system. */
10310 sh = jauRxp(r5h, s5h);
10311
10312 /* De-orient the Hipparcos position into the FK5 system. */
10313 pv5[0] = jauTrxp(r5h, pvh[0]);
10314
10315 /* Apply spin to the position giving an extra space motion component. */
10316 wxp = jauPxp(pvh[0],sh);
10317
10318 /* Subtract this component from the Hipparcos space motion. */
10319 vv = jauPmp(pvh[1], wxp);
10320
10321 /* De-orient the Hipparcos space motion into the FK5 system. */
10322 pv5[1] = jauTrxp(r5h, vv);
10323
10324 /* FK5 pv-vector to spherical., r5, d5, dr5, dd5, px5, rv5 */
10325 CatalogCoords cat = null;
10326 try {
10327 cat = jauPvstar(pv5);
10328 } catch (JSOFAInternalError e) {
10329 // original code just ignored this possibility
10330 e.printStackTrace();
10331 }
10332
10333 return cat;
10334
10335 }
10336
10337
10338 /**
10339 * Transform a Hipparcos star position into FK5 J2000.0, assuming
10340 * zero Hipparcos proper motion.
10341 *
10342 *<p>This function is derived from the International Astronomical Union's
10343 * SOFA (Standards Of Fundamental Astronomy) software collection.
10344 *
10345 *<p>Status: support function.
10346 *
10347 *<!-- Given: -->
10348 * @param rh double Hipparcos RA (radians)
10349 * @param dh double Hipparcos Dec (radians)
10350 * @param date1 double TDB date (Note 1)
10351 * @param date2 double TDB date (Note 1)
10352 *
10353 * FIXME original did not return the parallax and radial velocity of the CatalogCoords type.
10354 * Returned (all FK5, equinox J2000.0, date date1+date2):
10355 * r5 double RA (radians)
10356 * d5 double Dec (radians)
10357 * dr5 double FK5 RA proper motion (rad/year, Note 4)
10358 * dd5 double Dec proper motion (rad/year, Note 4)
10359 *
10360 * <p>Notes:
10361 * <ol>
10362 *
10363 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
10364 * convenient way between the two arguments. For example,
10365 * JD(TT)=2450123.7 could be expressed in any of these ways,
10366 * among others:
10367 *<pre>
10368 * date1 date2
10369 *
10370 * 2450123.7 0.0 (JD method)
10371 * 2451545.0 -1421.3 (J2000 method)
10372 * 2400000.5 50123.2 (MJD method)
10373 * 2450123.5 0.2 (date & time method)
10374 *</pre>
10375 * The JD method is the most natural and convenient to use in
10376 * cases where the loss of several decimal digits of resolution
10377 * is acceptable. The J2000 method is best matched to the way
10378 * the argument is handled internally and will deliver the
10379 * optimum resolution. The MJD method and the date & time methods
10380 * are both good compromises between resolution and convenience.
10381 *
10382 * <li> The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
10383 *
10384 * <li> The FK5 to Hipparcos transformation is modeled as a pure rotation
10385 * and spin; zonal errors in the FK5 catalogue are not taken into
10386 * account.
10387 *
10388 * <li> It was the intention that Hipparcos should be a close
10389 * approximation to an inertial frame, so that distant objects have
10390 * zero proper motion; such objects have (in general) non-zero
10391 * proper motion in FK5, and this function returns those fictitious
10392 * proper motions.
10393 *
10394 * <li> The position returned by this function is in the FK5 J2000.0
10395 * reference system but at date date1+date2.
10396 *
10397 * <li> See also jauFk52h, jauH2fk5, jauFk5zhz.
10398 *</ol>
10399 *<p>Called:<ul>
10400 * <li>{@link #jauS2c} spherical coordinates to unit vector
10401 * <li>{@link #jauFk5hip} FK5 to Hipparcos rotation and spin
10402 * <li>{@link #jauRxp} product of r-matrix and p-vector
10403 * <li>{@link #jauSxp} multiply p-vector by scalar
10404 * <li>{@link #jauRxr} product of two r-matrices
10405 * <li>{@link #jauTrxp} product of transpose of r-matrix and p-vector
10406 * <li>{@link #jauPxp} vector product of two p-vectors
10407 * <li>{@link #jauPv2s} pv-vector to spherical
10408 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
10409 * </ul>
10410 *<p>Reference:
10411 *
10412 * <p>F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739.
10413 *
10414 *@version 2009 December 17
10415 *
10416 * @since Release 20101201
10417 *
10418 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10419 *
10420 */
10421 public static CatalogCoords jauHfk5z(double rh, double dh, double date1, double date2)
10422 {
10423 double t, ph[] = new double[3], r5h[][] = new double[3][3], s5h[] = new double[3], sh[] = new double[3], vst[] = new double[3],
10424 rst[][] = new double[3][3], r5ht[][] = new double[3][3], pv5e[][] = new double[2][3], vv[] = new double[3];
10425
10426
10427 /* Time interval from fundamental epoch J2000.0 to given date (JY). */
10428 t = ((date1 - DJ00) + date2) / DJY;
10429
10430 /* Hipparcos barycentric position vector (normalized). */
10431 ph = jauS2c(rh,dh);
10432
10433 /* FK5 to Hipparcos orientation matrix and spin vector. */
10434 jauFk5hip(r5h, s5h);
10435
10436 /* Rotate the spin into the Hipparcos system. */
10437 sh = jauRxp(r5h, s5h);
10438
10439 /* Accumulated Hipparcos wrt FK5 spin over that interval. */
10440 vst = jauSxp(t,s5h);
10441
10442 /* Express the accumulated spin as a rotation matrix. */
10443 rst = jauRv2m(vst);
10444
10445 /* Rotation matrix: accumulated spin, then FK5 to Hipparcos. */
10446 r5ht = jauRxr(r5h, rst);
10447
10448 /* De-orient & de-spin the Hipparcos position into FK5 J2000.0. */
10449 pv5e[0] = jauTrxp(r5ht, ph);
10450
10451 /* Apply spin to the position giving a space motion. */
10452 vv = jauPxp(sh,ph);
10453
10454 /* De-orient & de-spin the Hipparcos space motion into FK5 J2000.0. */
10455 pv5e[1] = jauTrxp(r5ht, vv);
10456
10457 /* FK5 position/velocity pv-vector to spherical. */
10458 SphericalPositionVelocity pvs = jauPv2s(pv5e);
10459 double r5 = jauAnp(pvs.pos.theta);
10460
10461 return new CatalogCoords(r5, pvs.pos.phi, pvs.vel.theta, pvs.vel.phi, 0.0, 0.0);
10462
10463 }
10464
10465
10466 /**
10467 * Initialize an r-matrix to the identity matrix.
10468 *
10469 *<p>This function is derived from the International Astronomical Union's
10470 * SOFA (Standards Of Fundamental Astronomy) software collection.
10471 *
10472 *<p>Status: vector/matrix support function.
10473 *
10474 *<!-- Returned: -->
10475 * @param r double[3][3] <u>returned</u> r-matrix
10476 *
10477 *<p>Called:<ul>
10478 * <li>{@link #jauZr} zero r-matrix
10479 * </ul>
10480 *@version 2008 May 11
10481 *
10482 * @since Release 20101201
10483 *
10484 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10485 */
10486 public static void jauIr(double r[][])
10487 {
10488 jauZr(r);
10489 r[0][0] = 1.0;
10490 r[1][1] = 1.0;
10491 r[2][2] = 1.0;
10492
10493 return;
10494
10495 }
10496
10497
10498 /**
10499 * Julian Date to Gregorian year, month, day, and fraction of a day.
10500 *
10501 *<p>This function is derived from the International Astronomical Union's
10502 * SOFA (Standards Of Fundamental Astronomy) software collection.
10503 *
10504 *<p>Status: support function.
10505 *
10506 *<!-- Given: -->
10507 * @param dj1 double Julian Date (Notes 1, 2)
10508 * @param dj2 double Julian Date (Notes 1, 2)
10509 *
10510 * Returned (arguments):
10511 * iy int year
10512 * im int month
10513 * id int day
10514 * fd double fraction of day
10515 *
10516 * <!-- Returned (function value): -->
10517 * @return int status:
10518 * 0 = OK
10519 * -1 = unacceptable date (Note 3)
10520 *
10521 * <p>Notes:
10522 * <ol>
10523 *
10524 * <li> The earliest valid date is -68569.5 (-4900 March 1). The
10525 * largest value accepted is 10^9.
10526 *
10527 * <li> The Julian Date is apportioned in any convenient way between
10528 * the arguments dj1 and dj2. For example, JD=2450123.7 could
10529 * be expressed in any of these ways, among others:
10530 *<pre>
10531 * dj1 dj2
10532 *
10533 * 2450123.7 0.0 (JD method)
10534 * 2451545.0 -1421.3 (J2000 method)
10535 * 2400000.5 50123.2 (MJD method)
10536 * 2450123.5 0.2 (date & time method)
10537 *</pre>
10538 * <li> In early eras the conversion is from the "proleptic Gregorian
10539 * calendar"; no account is taken of the date(s) of adoption of
10540 * the Gregorian calendar, nor is the AD/BC numbering convention
10541 * observed.
10542 *</ol>
10543 *<p>Reference:
10544 *
10545 * <p>Explanatory Supplement to the Astronomical Almanac,
10546 * P. Kenneth Seidelmann (ed), University Science Books (1992),
10547 * Section 12.92 (p604).
10548 *
10549 *@version 2008 May 26
10550 *
10551 * @since Release 20101201
10552 *
10553 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10554 */
10555 public static Calendar jauJd2cal(double dj1, double dj2) throws JSOFAIllegalParameter
10556 {
10557 /* Minimum and maximum allowed JD */
10558 final double djmin = -68569.5;
10559 final double djmax = 1e9;
10560
10561 long jd, l, n, i, k;
10562 double dj, d1, d2, f1, f2, f, d;
10563
10564
10565 /* Verify date is acceptable. */
10566 dj = dj1 + dj2;
10567 if (dj < djmin || dj > djmax) throw new JSOFAIllegalParameter("input julian date out of range", -1);
10568
10569 /* Copy the date, big then small, and re-align to midnight. */
10570 if (dj1 >= dj2) {
10571 d1 = dj1;
10572 d2 = dj2;
10573 } else {
10574 d1 = dj2;
10575 d2 = dj1;
10576 }
10577 d2 -= 0.5;
10578
10579 /* Separate day and fraction. */
10580 f1 = fmod(d1, 1.0);
10581 f2 = fmod(d2, 1.0);
10582 f = fmod(f1 + f2, 1.0);
10583 if (f < 0.0) f += 1.0;
10584 d = floor(d1 - f1) + floor(d2 - f2) + floor(f1 + f2 - f);
10585 jd = (long) floor(d) + 1L;
10586
10587 /* Express day in Gregorian calendar. */
10588 l = jd + 68569L;
10589 n = (4L * l) / 146097L;
10590 l -= (146097L * n + 3L) / 4L;
10591 i = (4000L * (l + 1L)) / 1461001L;
10592 l -= (1461L * i) / 4L - 31L;
10593 k = (80L * l) / 2447L;
10594 int id = (int) (l - (2447L * k) / 80L);
10595 l = k / 11L;
10596 int im = (int) (k + 2L - 12L * l);
10597 int iy = (int) (100L * (n - 49L) + i + l);
10598
10599
10600 return new Calendar(iy, im, id, f);
10601
10602 }
10603
10604 /**
10605 * Julian Date to Gregorian Calendar, expressed in a form convenient
10606 * for formatting messages: rounded to a specified precision.
10607 *
10608 *<p>This function is derived from the International Astronomical Union's
10609 * SOFA (Standards Of Fundamental Astronomy) software collection.
10610 *
10611 *<p>Status: support function.
10612 *
10613 *<!-- Given: -->
10614 * @param ndp int number of decimal places of days in fraction
10615 * @param dj1 double dj1+dj2 = Julian Date (Note 1)
10616 * @param dj2 double dj1+dj2 = Julian Date (Note 1)
10617 *
10618 *<!-- Returned: -->
10619 * @param iymdf int[4] <u>returned</u> year, month, day, fraction in Gregorian calendar
10620 *
10621 *
10622 * <!-- Returned (function value): -->
10623 * @return int status:
10624 * -1 = date out of range
10625 * 0 = OK
10626 * +1 = NDP not 0-9 (interpreted as 0)
10627 *
10628 * <p>Notes:
10629 * <ol>
10630 *
10631 * <li> The Julian Date is apportioned in any convenient way between
10632 * the arguments dj1 and dj2. For example, JD=2450123.7 could
10633 * be expressed in any of these ways, among others:
10634 *<pre>
10635 * dj1 dj2
10636 *
10637 * 2450123.7 0.0 (JD method)
10638 * 2451545.0 -1421.3 (J2000 method)
10639 * 2400000.5 50123.2 (MJD method)
10640 * 2450123.5 0.2 (date & time method)
10641 *</pre>
10642 * <li> In early eras the conversion is from the "Proleptic Gregorian
10643 * Calendar"; no account is taken of the date(s) of adoption of
10644 * the Gregorian Calendar, nor is the AD/BC numbering convention
10645 * observed.
10646 *
10647 * <li> Refer to the function jauJd2cal.
10648 *
10649 * <li> NDP should be 4 or less if internal overflows are to be
10650 * avoided on machines which use 16-bit integers.
10651 *</ol>
10652 *<p>Called:<ul>
10653 * <li>{@link #jauJd2cal} JD to Gregorian calendar
10654 * </ul>
10655 *<p>Reference:
10656 *
10657 * <p>Explanatory Supplement to the Astronomical Almanac,
10658 * P. Kenneth Seidelmann (ed), University Science Books (1992),
10659 * Section 12.92 (p604).
10660 *
10661 *@version 2008 October 28
10662 *
10663 * @since Release 20101201
10664 *
10665 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10666 */
10667 public static int jauJdcalf(int ndp, double dj1, double dj2, int iymdf[])
10668 {
10669 int j;
10670 double denom, d1, d2, f1, f2, f;
10671
10672
10673 /* Denominator of fraction (e.g. 100 for 2 decimal places). */
10674 if ((ndp >= 0) && (ndp <= 9)) {
10675 j = 0;
10676 denom = pow(10.0, ndp);
10677 } else {
10678 j = 1;
10679 denom = 1.0;
10680 }
10681
10682 /* Copy the date, big then small, and realign to midnight. */
10683 if (dj1 >= dj2) {
10684 d1 = dj1;
10685 d2 = dj2;
10686 } else {
10687 d1 = dj2;
10688 d2 = dj1;
10689 }
10690 d2 -= 0.5;
10691
10692 /* Separate days and fractions. */
10693 f1 = fmod(d1, 1.0);
10694 f2 = fmod(d2, 1.0);
10695 d1 = floor(d1 - f1);
10696 d2 = floor(d2 - f2);
10697
10698 /* Round the total fraction to the specified number of places. */
10699 f = floor((f1 + f2) * denom) / denom;
10700
10701 /* Re-assemble the rounded date and re-align to noon. */
10702 d2 += f + 0.5;
10703
10704 /* Convert to Gregorian Calendar. */
10705 try {
10706 Calendar cal = jauJd2cal(d1, d2);
10707 iymdf[0] = cal.iy;
10708 iymdf[1] = cal.im;
10709 iymdf[2] = cal.id;
10710 iymdf[3] = (int) (cal.fd * denom);
10711 } catch (JSOFAIllegalParameter e) {
10712 j = -1;
10713 }
10714
10715 /* Return the status. */
10716 return j;
10717
10718 }
10719
10720
10721 /**
10722 * Form the matrix of nutation for a given date, IAU 2000A model.
10723 *
10724 *<p>This function is derived from the International Astronomical Union's
10725 * SOFA (Standards Of Fundamental Astronomy) software collection.
10726 *
10727 *<p>Status: support function.
10728 *
10729 *<!-- Given: -->
10730 * @param date1 double TT as a 2-part Julian Date (Note 1)
10731 * @param date2 double TT as a 2-part Julian Date (Note 1)
10732 *
10733 *<!-- Returned: -->
10734 * @return rmatn double[3][3] <u>returned</u> nutation matrix
10735 *
10736 * <p>Notes:
10737 * <ol>
10738 *
10739 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
10740 * convenient way between the two arguments. For example,
10741 * JD(TT)=2450123.7 could be expressed in any of these ways,
10742 * among others:
10743 *<pre>
10744 * date1 date2
10745 *
10746 * 2450123.7 0.0 (JD method)
10747 * 2451545.0 -1421.3 (J2000 method)
10748 * 2400000.5 50123.2 (MJD method)
10749 * 2450123.5 0.2 (date & time method)
10750 *</pre>
10751 * The JD method is the most natural and convenient to use in
10752 * cases where the loss of several decimal digits of resolution
10753 * is acceptable. The J2000 method is best matched to the way
10754 * the argument is handled internally and will deliver the
10755 * optimum resolution. The MJD method and the date & time methods
10756 * are both good compromises between resolution and convenience.
10757 *
10758 * <li> The matrix operates in the sense V(true) = rmatn * V(mean), where
10759 * the p-vector V(true) is with respect to the true equatorial triad
10760 * of date and the p-vector V(mean) is with respect to the mean
10761 * equatorial triad of date.
10762 *
10763 * <li> A faster, but slightly less accurate result (about 1 mas), can be
10764 * obtained by using instead the jauNum00b function.
10765 *</ol>
10766 *<p>Called:<ul>
10767 * <li>{@link #jauPn00a} bias/precession/nutation, IAU 2000A
10768 * </ul>
10769 *<p>Reference:
10770 *
10771 * <p>Explanatory Supplement to the Astronomical Almanac,
10772 * P. Kenneth Seidelmann (ed), University Science Books (1992),
10773 * Section 3.222-3 (p114).
10774 *
10775 *@version 2008 May 12
10776 *
10777 * @since Release 20101201
10778 *
10779 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10780 */
10781 public static double[][] jauNum00a(double date1, double date2)
10782 {
10783
10784 /* Obtain the required matrix (discarding other results). */
10785 PrecessionNutation pn = jauPn00a(date1, date2);
10786
10787 return pn.rn ;
10788
10789 }
10790
10791
10792 /**
10793 * Form the matrix of nutation for a given date, IAU 2000B model.
10794 *
10795 *<p>This function is derived from the International Astronomical Union's
10796 * SOFA (Standards Of Fundamental Astronomy) software collection.
10797 *
10798 *<p>Status: support function.
10799 *
10800 *<!-- Given: -->
10801 * @param date1 double TT as a 2-part Julian Date (Note 1)
10802 * @param date2 double TT as a 2-part Julian Date (Note 1)
10803 *
10804 *<!-- Returned: -->
10805 * @return rmatn double[3][3] <u>returned</u> nutation matrix
10806 *
10807 * <p>Notes:
10808 * <ol>
10809 *
10810 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
10811 * convenient way between the two arguments. For example,
10812 * JD(TT)=2450123.7 could be expressed in any of these ways,
10813 * among others:
10814 *<pre>
10815 * date1 date2
10816 *
10817 * 2450123.7 0.0 (JD method)
10818 * 2451545.0 -1421.3 (J2000 method)
10819 * 2400000.5 50123.2 (MJD method)
10820 * 2450123.5 0.2 (date & time method)
10821 *</pre>
10822 * The JD method is the most natural and convenient to use in
10823 * cases where the loss of several decimal digits of resolution
10824 * is acceptable. The J2000 method is best matched to the way
10825 * the argument is handled internally and will deliver the
10826 * optimum resolution. The MJD method and the date & time methods
10827 * are both good compromises between resolution and convenience.
10828 *
10829 * <li> The matrix operates in the sense V(true) = rmatn * V(mean), where
10830 * the p-vector V(true) is with respect to the true equatorial triad
10831 * of date and the p-vector V(mean) is with respect to the mean
10832 * equatorial triad of date.
10833 *
10834 * <li> The present function is faster, but slightly less accurate (about
10835 * 1 mas), than the jauNum00a function.
10836 *</ol>
10837 *<p>Called:<ul>
10838 * <li>{@link #jauPn00b} bias/precession/nutation, IAU 2000B
10839 * </ul>
10840 *<p>Reference:
10841 *
10842 * <p>Explanatory Supplement to the Astronomical Almanac,
10843 * P. Kenneth Seidelmann (ed), University Science Books (1992),
10844 * Section 3.222-3 (p114).
10845 *
10846 *@version 2008 May 12
10847 *
10848 * @since Release 20101201
10849 *
10850 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10851 */
10852 public static double[][] jauNum00b(double date1, double date2)
10853 {
10854
10855 /* Obtain the required matrix (discarding other results). */
10856 PrecessionNutation pn = jauPn00b(date1, date2);
10857
10858 return pn.rn;
10859
10860 }
10861
10862
10863 /**
10864 * Form the matrix of nutation for a given date, IAU 2006/2000A model.
10865 *
10866 *<p>This function is derived from the International Astronomical Union's
10867 * SOFA (Standards Of Fundamental Astronomy) software collection.
10868 *
10869 *<p>Status: support function.
10870 *
10871 *<!-- Given: -->
10872 * @param date1 double TT as a 2-part Julian Date (Note 1)
10873 * @param date2 double TT as a 2-part Julian Date (Note 1)
10874 *
10875 *<!-- Returned: -->
10876 * @return rmatn double[3][3] <u>returned</u> nutation matrix
10877 *
10878 * <p>Notes:
10879 * <ol>
10880 *
10881 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
10882 * convenient way between the two arguments. For example,
10883 * JD(TT)=2450123.7 could be expressed in any of these ways,
10884 * among others:
10885 *<pre>
10886 * date1 date2
10887 *
10888 * 2450123.7 0.0 (JD method)
10889 * 2451545.0 -1421.3 (J2000 method)
10890 * 2400000.5 50123.2 (MJD method)
10891 * 2450123.5 0.2 (date & time method)
10892 *</pre>
10893 * The JD method is the most natural and convenient to use in
10894 * cases where the loss of several decimal digits of resolution
10895 * is acceptable. The J2000 method is best matched to the way
10896 * the argument is handled internally and will deliver the
10897 * optimum resolution. The MJD method and the date & time methods
10898 * are both good compromises between resolution and convenience.
10899 *
10900 * <li> The matrix operates in the sense V(true) = rmatn * V(mean), where
10901 * the p-vector V(true) is with respect to the true equatorial triad
10902 * of date and the p-vector V(mean) is with respect to the mean
10903 * equatorial triad of date.
10904 *</ol>
10905 *<p>Called:<ul>
10906 * <li>{@link #jauObl06} mean obliquity, IAU 2006
10907 * <li>{@link #jauNut06a} nutation, IAU 2006/2000A
10908 * <li>{@link #jauNumat} form nutation matrix
10909 * </ul>
10910 *<p>Reference:
10911 *
10912 * <p>Explanatory Supplement to the Astronomical Almanac,
10913 * P. Kenneth Seidelmann (ed), University Science Books (1992),
10914 * Section 3.222-3 (p114).
10915 *
10916 *@version 2008 May 12
10917 *
10918 * @since Release 20101201
10919 *
10920 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10921 */
10922 public static double[][] jauNum06a(double date1, double date2)
10923 {
10924 double eps, rmatn[][];
10925
10926
10927 /* Mean obliquity. */
10928 eps = jauObl06(date1, date2);
10929
10930 /* Nutation components. */
10931 NutationTerms nut = jauNut06a(date1, date2);
10932
10933 /* Nutation matrix. */
10934 rmatn = jauNumat(eps, nut.dpsi, nut.deps);
10935
10936 return rmatn;
10937
10938 }
10939
10940
10941 /**
10942 * Form the matrix of nutation.
10943 *
10944 *<p>This function is derived from the International Astronomical Union's
10945 * SOFA (Standards Of Fundamental Astronomy) software collection.
10946 *
10947 *<p>Status: support function.
10948 *
10949 *<!-- Given: -->
10950 * @param epsa double mean obliquity of date (Note 1)
10951 * @param dpsi double nutation (Note 2)
10952 * @param deps double nutation (Note 2)
10953 *
10954 *<!-- Returned: -->
10955 * @return rmatn double[3][3] <u>returned</u> nutation matrix (Note 3)
10956 *
10957 * <p>Notes:
10958 * <ol>
10959 *
10960 *
10961 * <li> The supplied mean obliquity epsa, must be consistent with the
10962 * precession-nutation models from which dpsi and deps were obtained.
10963 *
10964 * <li> The caller is responsible for providing the nutation components;
10965 * they are in longitude and obliquity, in radians and are with
10966 * respect to the equinox and ecliptic of date.
10967 *
10968 * <li> The matrix operates in the sense V(true) = rmatn * V(mean),
10969 * where the p-vector V(true) is with respect to the true
10970 * equatorial triad of date and the p-vector V(mean) is with
10971 * respect to the mean equatorial triad of date.
10972 *</ol>
10973 *<p>Called:<ul>
10974 * <li>{@link #jauIr} initialize r-matrix to identity
10975 * <li>{@link #jauRx} rotate around X-axis
10976 * <li>{@link #jauRz} rotate around Z-axis
10977 * </ul>
10978 *<p>Reference:
10979 *
10980 * <p>Explanatory Supplement to the Astronomical Almanac,
10981 * P. Kenneth Seidelmann (ed), University Science Books (1992),
10982 * Section 3.222-3 (p114).
10983 *
10984 *@version 2008 May 11
10985 *
10986 * @since Release 20101201
10987 *
10988 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10989 */
10990 public static double[][] jauNumat(double epsa, double dpsi, double deps)
10991 {
10992 double rmatn[][] = new double[3][3];
10993 /* Build the rotation matrix. */
10994 jauIr(rmatn);
10995 jauRx(epsa, rmatn);
10996 jauRz(-dpsi, rmatn);
10997 jauRx(-(epsa + deps), rmatn);
10998
10999 return rmatn;
11000
11001 }
11002 /**
11003 * Nutation Terms.
11004 * .
11005 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 21 Nov 2011
11006 * @version $Revision$ $date$
11007 */
11008 public static class NutationTerms {
11009 /** nutation component in longitude */
11010 public double dpsi;
11011 /** nutation component in obliquity */
11012 public double deps;
11013 public NutationTerms(double dpsi, double deps) {
11014 this.dpsi = dpsi;
11015 this.deps = deps;
11016 }
11017 }
11018 /**
11019 * Nutation, IAU 2000A model (MHB2000 luni-solar and planetary nutation
11020 * with free core nutation omitted).
11021 *
11022 *<p>This function is derived from the International Astronomical Union's
11023 * SOFA (Standards Of Fundamental Astronomy) software collection.
11024 *
11025 *<p>Status: canonical model.
11026 *
11027 *<!-- Given: -->
11028 * @param date1 double TT as a 2-part Julian Date (Note 1)
11029 * @param date2 double TT as a 2-part Julian Date (Note 1)
11030 *
11031 *<!-- Returned: -->
11032 * @return <u>returned</u> nutation, luni-solar + planetary (Note 2)
11033 *
11034 * <p>Notes:
11035 * <ol>
11036 *
11037 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
11038 * convenient way between the two arguments. For example,
11039 * JD(TT)=2450123.7 could be expressed in any of these ways,
11040 * among others:
11041 *<pre>
11042 * date1 date2
11043 *
11044 * 2450123.7 0.0 (JD method)
11045 * 2451545.0 -1421.3 (J2000 method)
11046 * 2400000.5 50123.2 (MJD method)
11047 * 2450123.5 0.2 (date & time method)
11048 *</pre>
11049 * The JD method is the most natural and convenient to use in
11050 * cases where the loss of several decimal digits of resolution
11051 * is acceptable. The J2000 method is best matched to the way
11052 * the argument is handled internally and will deliver the
11053 * optimum resolution. The MJD method and the date & time methods
11054 * are both good compromises between resolution and convenience.
11055 *
11056 * <li> The nutation components in longitude and obliquity are in radians
11057 * and with respect to the equinox and ecliptic of date. The
11058 * obliquity at J2000.0 is assumed to be the Lieske et al. (1977)
11059 * value of 84381.448 arcsec.
11060 *
11061 * Both the luni-solar and planetary nutations are included. The
11062 * latter are due to direct planetary nutations and the
11063 * perturbations of the lunar and terrestrial orbits.
11064 *
11065 * <li> The function computes the MHB2000 nutation series with the
11066 * associated corrections for planetary nutations. It is an
11067 * implementation of the nutation part of the IAU 2000A precession-
11068 * nutation model, formally adopted by the IAU General Assembly in
11069 * 2000, namely MHB2000 (Mathews et al. 2002), but with the free
11070 * core nutation (FCN - see Note 4) omitted.
11071 *
11072 * <li> The full MHB2000 model also contains contributions to the
11073 * nutations in longitude and obliquity due to the free-excitation
11074 * of the free-core-nutation during the period 1979-2000. These FCN
11075 * terms, which are time-dependent and unpredictable, are NOT
11076 * included in the present function and, if required, must be
11077 * independently computed. With the FCN corrections included, the
11078 * present function delivers a pole which is at current epochs
11079 * accurate to a few hundred microarcseconds. The omission of FCN
11080 * introduces further errors of about that size.
11081 *
11082 * <li> The present function provides classical nutation. The MHB2000
11083 * algorithm, from which it is adapted, deals also with (i) the
11084 * offsets between the GCRS and mean poles and (ii) the adjustments
11085 * in longitude and obliquity due to the changed precession rates.
11086 * These additional functions, namely frame bias and precession
11087 * adjustments, are supported by the JSOFA functions jauBi00 and
11088 * jauPr00.
11089 *
11090 * <li> The MHB2000 algorithm also provides "total" nutations, comprising
11091 * the arithmetic sum of the frame bias, precession adjustments,
11092 * luni-solar nutation and planetary nutation. These total
11093 * nutations can be used in combination with an existing IAU 1976
11094 * precession implementation, such as jauPmat76, to deliver GCRS-
11095 * to-true predictions of sub-mas accuracy at current dates.
11096 * However, there are three shortcomings in the MHB2000 model that
11097 * must be taken into account if more accurate or definitive results
11098 * are required (see Wallace 2002):
11099 *
11100 * (i) The MHB2000 total nutations are simply arithmetic sums,
11101 * yet in reality the various components are successive Euler
11102 * rotations. This slight lack of rigor leads to cross terms
11103 * that exceed 1 mas after a century. The rigorous procedure
11104 * is to form the GCRS-to-true rotation matrix by applying the
11105 * bias, precession and nutation in that order.
11106 *
11107 * (ii) Although the precession adjustments are stated to be with
11108 * respect to Lieske et al. (1977), the MHB2000 model does
11109 * not specify which set of Euler angles are to be used and
11110 * how the adjustments are to be applied. The most literal
11111 * and straightforward procedure is to adopt the 4-rotation
11112 * epsilon_0, psi_A, omega_A, xi_A option, and to add DPSIPR
11113 * to psi_A and DEPSPR to both omega_A and eps_A.
11114 *
11115 * (iii) The MHB2000 model predates the determination by Chapront
11116 * et al. (2002) of a 14.6 mas displacement between the
11117 * J2000.0 mean equinox and the origin of the ICRS frame. It
11118 * should, however, be noted that neglecting this displacement
11119 * when calculating star coordinates does not lead to a
11120 * 14.6 mas change in right ascension, only a small second-
11121 * order distortion in the pattern of the precession-nutation
11122 * effect.
11123 *
11124 * For these reasons, the JSOFA functions do not generate the "total
11125 * nutations" directly, though they can of course easily be
11126 * generated by calling jauBi00, jauPr00 and the present function
11127 * and adding the results.
11128 *
11129 * <li> The MHB2000 model contains 41 instances where the same frequency
11130 * appears multiple times, of which 38 are duplicates and three are
11131 * triplicates. To keep the present code close to the original MHB
11132 * algorithm, this small inefficiency has not been corrected.
11133 *</ol>
11134 *<p>Called:<ul>
11135 * <li>{@link #jauFal03} mean anomaly of the Moon
11136 * <li>{@link #jauFaf03} mean argument of the latitude of the Moon
11137 * <li>{@link #jauFaom03} mean longitude of the Moon's ascending node
11138 * <li>{@link #jauFame03} mean longitude of Mercury
11139 * <li>{@link #jauFave03} mean longitude of Venus
11140 * <li>{@link #jauFae03} mean longitude of Earth
11141 * <li>{@link #jauFama03} mean longitude of Mars
11142 * <li>{@link #jauFaju03} mean longitude of Jupiter
11143 * <li>{@link #jauFasa03} mean longitude of Saturn
11144 * <li>{@link #jauFaur03} mean longitude of Uranus
11145 * <li>{@link #jauFapa03} general accumulated precession in longitude
11146 * </ul>
11147 *<p>References:
11148 *
11149 * <p>Chapront, J., Chapront-Touze, M. & Francou, G. 2002,
11150 * Astron.Astrophys. 387, 700
11151 *
11152 * <p>Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977,
11153 * Astron.Astrophys. 58, 1-16
11154 *
11155 * <p>Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res.
11156 * 107, B4. The MHB_2000 code itself was obtained on 9th September
11157 * 2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
11158 *
11159 * <p>Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
11160 * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
11161 *
11162 * <p>Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
11163 * Astron.Astrophys.Supp.Ser. 135, 111
11164 *
11165 * <p>Wallace, P.T., "Software for Implementing the IAU 2000
11166 * Resolutions", in IERS Workshop 5.1 (2002)
11167 *
11168 *@version 2009 December 17
11169 *
11170 * @since Release 20101201
11171 *
11172 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
11173 */
11174 public static NutationTerms jauNut00a(double date1, double date2 )
11175 {
11176 int i;
11177 double t, el, elp, f, d, om, arg, dp, de, sarg, carg,
11178 al, af, ad, aom, alme, alve, alea, alma,
11179 alju, alsa, alur, alne, apa, dpsils, depsls,
11180 dpsipl, depspl;
11181
11182 /* Units of 0.1 microarcsecond to radians */
11183 final double U2R = DAS2R / 1e7;
11184
11185 /* ------------------------- */
11186 /* Luni-Solar nutation model */
11187 /* ------------------------- */
11188
11189 /* The units for the sine and cosine coefficients are */
11190 /* 0.1 microarcsecond and the same per Julian century */
11191
11192 final class NutationModel {
11193 int nl,nlp,nf,nd,nom; /* coefficients of l,l',F,D,Om */
11194 double sp,spt,cp; /* longitude sin, t*sin, cos coefficients */
11195 double ce,cet,se; /* obliquity cos, t*cos, sin coefficients */
11196 public NutationModel(int nl,int nlp,int nf,int nd, int nom,
11197 double sp,double spt,double cp,
11198 double ce,double cet,double se ) {
11199 this.nl = nl;
11200 this.nlp = nlp;
11201 this.nf = nf;
11202 this.nd = nd;
11203 this.nom = nom;
11204 this.sp = sp;
11205 this.spt = spt;
11206 this.cp = cp;
11207 this.ce = ce;
11208 this.cet = cet;
11209 this.se = se;
11210 }
11211 }
11212
11213 NutationModel xls[] = {
11214
11215 /* 1- 10 */
11216 new NutationModel( 0, 0, 0, 0, 1,
11217 -172064161.0, -174666.0, 33386.0, 92052331.0, 9086.0, 15377.0),
11218 new NutationModel( 0, 0, 2,-2, 2,
11219 -13170906.0, -1675.0, -13696.0, 5730336.0, -3015.0, -4587.0),
11220 new NutationModel( 0, 0, 2, 0, 2,-2276413.0,-234.0,2796.0,978459.0,-485.0, 1374.0),
11221 new NutationModel( 0, 0, 0, 0, 2,2074554.0, 207.0, -698.0,-897492.0,470.0, -291.0),
11222 new NutationModel( 0, 1, 0, 0, 0,1475877.0,-3633.0,11817.0,73871.0,-184.0,-1924.0),
11223 new NutationModel( 0, 1, 2,-2, 2,-516821.0,1226.0, -524.0,224386.0,-677.0, -174.0),
11224 new NutationModel( 1, 0, 0, 0, 0, 711159.0, 73.0, -872.0, -6750.0, 0.0, 358.0),
11225 new NutationModel( 0, 0, 2, 0, 1,-387298.0,-367.0, 380.0, 200728.0, 18.0, 318.0),
11226 new NutationModel( 1, 0, 2, 0, 2,-301461.0, -36.0, 816.0, 129025.0,-63.0, 367.0),
11227 new NutationModel( 0,-1, 2,-2, 2, 215829.0,-494.0, 111.0, -95929.0,299.0, 132.0),
11228
11229 /* 11-20 */
11230 new NutationModel( 0, 0, 2,-2, 1, 128227.0, 137.0, 181.0, -68982.0, -9.0, 39.0),
11231 new NutationModel(-1, 0, 2, 0, 2, 123457.0, 11.0, 19.0, -53311.0, 32.0, -4.0),
11232 new NutationModel(-1, 0, 0, 2, 0, 156994.0, 10.0, -168.0, -1235.0, 0.0, 82.0),
11233 new NutationModel( 1, 0, 0, 0, 1, 63110.0, 63.0, 27.0, -33228.0, 0.0, -9.0),
11234 new NutationModel(-1, 0, 0, 0, 1, -57976.0, -63.0, -189.0, 31429.0, 0.0, -75.0),
11235 new NutationModel(-1, 0, 2, 2, 2, -59641.0, -11.0, 149.0, 25543.0,-11.0, 66.0),
11236 new NutationModel( 1, 0, 2, 0, 1, -51613.0, -42.0, 129.0, 26366.0, 0.0, 78.0),
11237 new NutationModel(-2, 0, 2, 0, 1, 45893.0, 50.0, 31.0, -24236.0,-10.0, 20.0),
11238 new NutationModel( 0, 0, 0, 2, 0, 63384.0, 11.0, -150.0, -1220.0, 0.0, 29.0),
11239 new NutationModel( 0, 0, 2, 2, 2, -38571.0, -1.0, 158.0, 16452.0,-11.0, 68.0),
11240
11241 /* 21-30 */
11242 new NutationModel( 0,-2, 2,-2, 2, 32481.0, 0.0, 0.0, -13870.0, 0.0, 0.0),
11243 new NutationModel(-2, 0, 0, 2, 0, -47722.0, 0.0, -18.0, 477.0, 0.0, -25.0),
11244 new NutationModel( 2, 0, 2, 0, 2, -31046.0, -1.0, 131.0, 13238.0,-11.0, 59.0),
11245 new NutationModel( 1, 0, 2,-2, 2, 28593.0, 0.0, -1.0, -12338.0, 10.0, -3.0),
11246 new NutationModel(-1, 0, 2, 0, 1, 20441.0, 21.0, 10.0, -10758.0, 0.0, -3.0),
11247 new NutationModel( 2, 0, 0, 0, 0, 29243.0, 0.0, -74.0, -609.0, 0.0, 13.0),
11248 new NutationModel( 0, 0, 2, 0, 0, 25887.0, 0.0, -66.0, -550.0, 0.0, 11.0),
11249 new NutationModel( 0, 1, 0, 0, 1, -14053.0, -25.0, 79.0, 8551.0, -2.0, -45.0),
11250 new NutationModel(-1, 0, 0, 2, 1, 15164.0, 10.0, 11.0, -8001.0, 0.0, -1.0),
11251 new NutationModel( 0, 2, 2,-2, 2, -15794.0, 72.0, -16.0, 6850.0,-42.0, -5.0),
11252
11253 /* 31-40 */
11254 new NutationModel( 0, 0,-2, 2, 0, 21783.0, 0.0, 13.0, -167.0, 0.0, 13.0),
11255 new NutationModel( 1, 0, 0,-2, 1, -12873.0, -10.0, -37.0, 6953.0, 0.0, -14.0),
11256 new NutationModel( 0,-1, 0, 0, 1, -12654.0, 11.0, 63.0, 6415.0, 0.0, 26.0),
11257 new NutationModel(-1, 0, 2, 2, 1, -10204.0, 0.0, 25.0, 5222.0, 0.0, 15.0),
11258 new NutationModel( 0, 2, 0, 0, 0, 16707.0, -85.0, -10.0, 168.0, -1.0, 10.0),
11259 new NutationModel( 1, 0, 2, 2, 2, -7691.0, 0.0, 44.0, 3268.0, 0.0, 19.0),
11260 new NutationModel(-2, 0, 2, 0, 0, -11024.0, 0.0, -14.0, 104.0, 0.0, 2.0),
11261 new NutationModel( 0, 1, 2, 0, 2, 7566.0, -21.0, -11.0, -3250.0, 0.0, -5.0),
11262 new NutationModel( 0, 0, 2, 2, 1, -6637.0, -11.0, 25.0, 3353.0, 0.0, 14.0),
11263 new NutationModel( 0,-1, 2, 0, 2, -7141.0, 21.0, 8.0, 3070.0, 0.0, 4.0),
11264
11265 /* 41-50 */
11266 new NutationModel( 0, 0, 0, 2, 1, -6302.0, -11.0, 2.0, 3272.0, 0.0, 4.0),
11267 new NutationModel( 1, 0, 2,-2, 1, 5800.0, 10.0, 2.0, -3045.0, 0.0, -1.0),
11268 new NutationModel( 2, 0, 2,-2, 2, 6443.0, 0.0, -7.0, -2768.0, 0.0, -4.0),
11269 new NutationModel(-2, 0, 0, 2, 1, -5774.0, -11.0, -15.0, 3041.0, 0.0, -5.0),
11270 new NutationModel( 2, 0, 2, 0, 1, -5350.0, 0.0, 21.0, 2695.0, 0.0, 12.0),
11271 new NutationModel( 0,-1, 2,-2, 1, -4752.0, -11.0, -3.0, 2719.0, 0.0, -3.0),
11272 new NutationModel( 0, 0, 0,-2, 1, -4940.0, -11.0, -21.0, 2720.0, 0.0, -9.0),
11273 new NutationModel(-1,-1, 0, 2, 0, 7350.0, 0.0, -8.0, -51.0, 0.0, 4.0),
11274 new NutationModel( 2, 0, 0,-2, 1, 4065.0, 0.0, 6.0, -2206.0, 0.0, 1.0),
11275 new NutationModel( 1, 0, 0, 2, 0, 6579.0, 0.0, -24.0, -199.0, 0.0, 2.0),
11276
11277 /* 51-60 */
11278 new NutationModel( 0, 1, 2,-2, 1, 3579.0, 0.0, 5.0, -1900.0, 0.0, 1.0),
11279 new NutationModel( 1,-1, 0, 0, 0, 4725.0, 0.0, -6.0, -41.0, 0.0, 3.0),
11280 new NutationModel(-2, 0, 2, 0, 2, -3075.0, 0.0, -2.0, 1313.0, 0.0, -1.0),
11281 new NutationModel( 3, 0, 2, 0, 2, -2904.0, 0.0, 15.0, 1233.0, 0.0, 7.0),
11282 new NutationModel( 0,-1, 0, 2, 0, 4348.0, 0.0, -10.0, -81.0, 0.0, 2.0),
11283 new NutationModel( 1,-1, 2, 0, 2, -2878.0, 0.0, 8.0, 1232.0, 0.0, 4.0),
11284 new NutationModel( 0, 0, 0, 1, 0, -4230.0, 0.0, 5.0, -20.0, 0.0, -2.0),
11285 new NutationModel(-1,-1, 2, 2, 2, -2819.0, 0.0, 7.0, 1207.0, 0.0, 3.0),
11286 new NutationModel(-1, 0, 2, 0, 0, -4056.0, 0.0, 5.0, 40.0, 0.0, -2.0),
11287 new NutationModel( 0,-1, 2, 2, 2, -2647.0, 0.0, 11.0, 1129.0, 0.0, 5.0),
11288
11289 /* 61-70 */
11290 new NutationModel(-2, 0, 0, 0, 1, -2294.0, 0.0, -10.0, 1266.0, 0.0, -4.0),
11291 new NutationModel( 1, 1, 2, 0, 2, 2481.0, 0.0, -7.0, -1062.0, 0.0, -3.0),
11292 new NutationModel( 2, 0, 0, 0, 1, 2179.0, 0.0, -2.0, -1129.0, 0.0, -2.0),
11293 new NutationModel(-1, 1, 0, 1, 0, 3276.0, 0.0, 1.0, -9.0, 0.0, 0.0),
11294 new NutationModel( 1, 1, 0, 0, 0, -3389.0, 0.0, 5.0, 35.0, 0.0, -2.0),
11295 new NutationModel( 1, 0, 2, 0, 0, 3339.0, 0.0, -13.0, -107.0, 0.0, 1.0),
11296 new NutationModel(-1, 0, 2,-2, 1, -1987.0, 0.0, -6.0, 1073.0, 0.0, -2.0),
11297 new NutationModel( 1, 0, 0, 0, 2, -1981.0, 0.0, 0.0, 854.0, 0.0, 0.0),
11298 new NutationModel(-1, 0, 0, 1, 0, 4026.0, 0.0, -353.0, -553.0, 0.0, -139.0),
11299 new NutationModel( 0, 0, 2, 1, 2, 1660.0, 0.0, -5.0, -710.0, 0.0, -2.0),
11300
11301 /* 71-80 */
11302 new NutationModel(-1, 0, 2, 4, 2, -1521.0, 0.0, 9.0, 647.0, 0.0, 4.0),
11303 new NutationModel(-1, 1, 0, 1, 1, 1314.0, 0.0, 0.0, -700.0, 0.0, 0.0),
11304 new NutationModel( 0,-2, 2,-2, 1, -1283.0, 0.0, 0.0, 672.0, 0.0, 0.0),
11305 new NutationModel( 1, 0, 2, 2, 1, -1331.0, 0.0, 8.0, 663.0, 0.0, 4.0),
11306 new NutationModel(-2, 0, 2, 2, 2, 1383.0, 0.0, -2.0, -594.0, 0.0, -2.0),
11307 new NutationModel(-1, 0, 0, 0, 2, 1405.0, 0.0, 4.0, -610.0, 0.0, 2.0),
11308 new NutationModel( 1, 1, 2,-2, 2, 1290.0, 0.0, 0.0, -556.0, 0.0, 0.0),
11309 new NutationModel(-2, 0, 2, 4, 2, -1214.0, 0.0, 5.0, 518.0, 0.0, 2.0),
11310 new NutationModel(-1, 0, 4, 0, 2, 1146.0, 0.0, -3.0, -490.0, 0.0, -1.0),
11311 new NutationModel( 2, 0, 2,-2, 1, 1019.0, 0.0, -1.0, -527.0, 0.0, -1.0),
11312
11313 /* 81-90 */
11314 new NutationModel( 2, 0, 2, 2, 2, -1100.0, 0.0, 9.0, 465.0, 0.0, 4.0),
11315 new NutationModel( 1, 0, 0, 2, 1, -970.0, 0.0, 2.0, 496.0, 0.0, 1.0),
11316 new NutationModel( 3, 0, 0, 0, 0, 1575.0, 0.0, -6.0, -50.0, 0.0, 0.0),
11317 new NutationModel( 3, 0, 2,-2, 2, 934.0, 0.0, -3.0, -399.0, 0.0, -1.0),
11318 new NutationModel( 0, 0, 4,-2, 2, 922.0, 0.0, -1.0, -395.0, 0.0, -1.0),
11319 new NutationModel( 0, 1, 2, 0, 1, 815.0, 0.0, -1.0, -422.0, 0.0, -1.0),
11320 new NutationModel( 0, 0,-2, 2, 1, 834.0, 0.0, 2.0, -440.0, 0.0, 1.0),
11321 new NutationModel( 0, 0, 2,-2, 3, 1248.0, 0.0, 0.0, -170.0, 0.0, 1.0),
11322 new NutationModel(-1, 0, 0, 4, 0, 1338.0, 0.0, -5.0, -39.0, 0.0, 0.0),
11323 new NutationModel( 2, 0,-2, 0, 1, 716.0, 0.0, -2.0, -389.0, 0.0, -1.0),
11324
11325 /* 91-100 */
11326 new NutationModel(-2, 0, 0, 4, 0, 1282.0, 0.0, -3.0, -23.0, 0.0, 1.0),
11327 new NutationModel(-1,-1, 0, 2, 1, 742.0, 0.0, 1.0, -391.0, 0.0, 0.0),
11328 new NutationModel(-1, 0, 0, 1, 1, 1020.0, 0.0, -25.0, -495.0, 0.0, -10.0),
11329 new NutationModel( 0, 1, 0, 0, 2, 715.0, 0.0, -4.0, -326.0, 0.0, 2.0),
11330 new NutationModel( 0, 0,-2, 0, 1, -666.0, 0.0, -3.0, 369.0, 0.0, -1.0),
11331 new NutationModel( 0,-1, 2, 0, 1, -667.0, 0.0, 1.0, 346.0, 0.0, 1.0),
11332 new NutationModel( 0, 0, 2,-1, 2, -704.0, 0.0, 0.0, 304.0, 0.0, 0.0),
11333 new NutationModel( 0, 0, 2, 4, 2, -694.0, 0.0, 5.0, 294.0, 0.0, 2.0),
11334 new NutationModel(-2,-1, 0, 2, 0, -1014.0, 0.0, -1.0, 4.0, 0.0, -1.0),
11335 new NutationModel( 1, 1, 0,-2, 1, -585.0, 0.0, -2.0, 316.0, 0.0, -1.0),
11336
11337 /* 101-110 */
11338 new NutationModel(-1, 1, 0, 2, 0, -949.0, 0.0, 1.0, 8.0, 0.0, -1.0),
11339 new NutationModel(-1, 1, 0, 1, 2, -595.0, 0.0, 0.0, 258.0, 0.0, 0.0),
11340 new NutationModel( 1,-1, 0, 0, 1, 528.0, 0.0, 0.0, -279.0, 0.0, 0.0),
11341 new NutationModel( 1,-1, 2, 2, 2, -590.0, 0.0, 4.0, 252.0, 0.0, 2.0),
11342 new NutationModel(-1, 1, 2, 2, 2, 570.0, 0.0, -2.0, -244.0, 0.0, -1.0),
11343 new NutationModel( 3, 0, 2, 0, 1, -502.0, 0.0, 3.0, 250.0, 0.0, 2.0),
11344 new NutationModel( 0, 1,-2, 2, 0, -875.0, 0.0, 1.0, 29.0, 0.0, 0.0),
11345 new NutationModel(-1, 0, 0,-2, 1, -492.0, 0.0, -3.0, 275.0, 0.0, -1.0),
11346 new NutationModel( 0, 1, 2, 2, 2, 535.0, 0.0, -2.0, -228.0, 0.0, -1.0),
11347 new NutationModel(-1,-1, 2, 2, 1, -467.0, 0.0, 1.0, 240.0, 0.0, 1.0),
11348
11349 /* 111-120 */
11350 new NutationModel( 0,-1, 0, 0, 2, 591.0, 0.0, 0.0, -253.0, 0.0, 0.0),
11351 new NutationModel( 1, 0, 2,-4, 1, -453.0, 0.0, -1.0, 244.0, 0.0, -1.0),
11352 new NutationModel(-1, 0,-2, 2, 0, 766.0, 0.0, 1.0, 9.0, 0.0, 0.0),
11353 new NutationModel( 0,-1, 2, 2, 1, -446.0, 0.0, 2.0, 225.0, 0.0, 1.0),
11354 new NutationModel( 2,-1, 2, 0, 2, -488.0, 0.0, 2.0, 207.0, 0.0, 1.0),
11355 new NutationModel( 0, 0, 0, 2, 2, -468.0, 0.0, 0.0, 201.0, 0.0, 0.0),
11356 new NutationModel( 1,-1, 2, 0, 1, -421.0, 0.0, 1.0, 216.0, 0.0, 1.0),
11357 new NutationModel(-1, 1, 2, 0, 2, 463.0, 0.0, 0.0, -200.0, 0.0, 0.0),
11358 new NutationModel( 0, 1, 0, 2, 0, -673.0, 0.0, 2.0, 14.0, 0.0, 0.0),
11359 new NutationModel( 0,-1,-2, 2, 0, 658.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11360
11361 /* 121-130 */
11362 new NutationModel( 0, 3, 2,-2, 2, -438.0, 0.0, 0.0, 188.0, 0.0, 0.0),
11363 new NutationModel( 0, 0, 0, 1, 1, -390.0, 0.0, 0.0, 205.0, 0.0, 0.0),
11364 new NutationModel(-1, 0, 2, 2, 0, 639.0, -11.0, -2.0, -19.0, 0.0, 0.0),
11365 new NutationModel( 2, 1, 2, 0, 2, 412.0, 0.0, -2.0, -176.0, 0.0, -1.0),
11366 new NutationModel( 1, 1, 0, 0, 1, -361.0, 0.0, 0.0, 189.0, 0.0, 0.0),
11367 new NutationModel( 1, 1, 2, 0, 1, 360.0, 0.0, -1.0, -185.0, 0.0, -1.0),
11368 new NutationModel( 2, 0, 0, 2, 0, 588.0, 0.0, -3.0, -24.0, 0.0, 0.0),
11369 new NutationModel( 1, 0,-2, 2, 0, -578.0, 0.0, 1.0, 5.0, 0.0, 0.0),
11370 new NutationModel(-1, 0, 0, 2, 2, -396.0, 0.0, 0.0, 171.0, 0.0, 0.0),
11371 new NutationModel( 0, 1, 0, 1, 0, 565.0, 0.0, -1.0, -6.0, 0.0, 0.0),
11372
11373 /* 131-140 */
11374 new NutationModel( 0, 1, 0,-2, 1, -335.0, 0.0, -1.0, 184.0, 0.0, -1.0),
11375 new NutationModel(-1, 0, 2,-2, 2, 357.0, 0.0, 1.0, -154.0, 0.0, 0.0),
11376 new NutationModel( 0, 0, 0,-1, 1, 321.0, 0.0, 1.0, -174.0, 0.0, 0.0),
11377 new NutationModel(-1, 1, 0, 0, 1, -301.0, 0.0, -1.0, 162.0, 0.0, 0.0),
11378 new NutationModel( 1, 0, 2,-1, 2, -334.0, 0.0, 0.0, 144.0, 0.0, 0.0),
11379 new NutationModel( 1,-1, 0, 2, 0, 493.0, 0.0, -2.0, -15.0, 0.0, 0.0),
11380 new NutationModel( 0, 0, 0, 4, 0, 494.0, 0.0, -2.0, -19.0, 0.0, 0.0),
11381 new NutationModel( 1, 0, 2, 1, 2, 337.0, 0.0, -1.0, -143.0, 0.0, -1.0),
11382 new NutationModel( 0, 0, 2, 1, 1, 280.0, 0.0, -1.0, -144.0, 0.0, 0.0),
11383 new NutationModel( 1, 0, 0,-2, 2, 309.0, 0.0, 1.0, -134.0, 0.0, 0.0),
11384
11385 /* 141-150 */
11386 new NutationModel(-1, 0, 2, 4, 1, -263.0, 0.0, 2.0, 131.0, 0.0, 1.0),
11387 new NutationModel( 1, 0,-2, 0, 1, 253.0, 0.0, 1.0, -138.0, 0.0, 0.0),
11388 new NutationModel( 1, 1, 2,-2, 1, 245.0, 0.0, 0.0, -128.0, 0.0, 0.0),
11389 new NutationModel( 0, 0, 2, 2, 0, 416.0, 0.0, -2.0, -17.0, 0.0, 0.0),
11390 new NutationModel(-1, 0, 2,-1, 1, -229.0, 0.0, 0.0, 128.0, 0.0, 0.0),
11391 new NutationModel(-2, 0, 2, 2, 1, 231.0, 0.0, 0.0, -120.0, 0.0, 0.0),
11392 new NutationModel( 4, 0, 2, 0, 2, -259.0, 0.0, 2.0, 109.0, 0.0, 1.0),
11393 new NutationModel( 2,-1, 0, 0, 0, 375.0, 0.0, -1.0, -8.0, 0.0, 0.0),
11394 new NutationModel( 2, 1, 2,-2, 2, 252.0, 0.0, 0.0, -108.0, 0.0, 0.0),
11395 new NutationModel( 0, 1, 2, 1, 2, -245.0, 0.0, 1.0, 104.0, 0.0, 0.0),
11396
11397 /* 151-160 */
11398 new NutationModel( 1, 0, 4,-2, 2, 243.0, 0.0, -1.0, -104.0, 0.0, 0.0),
11399 new NutationModel(-1,-1, 0, 0, 1, 208.0, 0.0, 1.0, -112.0, 0.0, 0.0),
11400 new NutationModel( 0, 1, 0, 2, 1, 199.0, 0.0, 0.0, -102.0, 0.0, 0.0),
11401 new NutationModel(-2, 0, 2, 4, 1, -208.0, 0.0, 1.0, 105.0, 0.0, 0.0),
11402 new NutationModel( 2, 0, 2, 0, 0, 335.0, 0.0, -2.0, -14.0, 0.0, 0.0),
11403 new NutationModel( 1, 0, 0, 1, 0, -325.0, 0.0, 1.0, 7.0, 0.0, 0.0),
11404 new NutationModel(-1, 0, 0, 4, 1, -187.0, 0.0, 0.0, 96.0, 0.0, 0.0),
11405 new NutationModel(-1, 0, 4, 0, 1, 197.0, 0.0, -1.0, -100.0, 0.0, 0.0),
11406 new NutationModel( 2, 0, 2, 2, 1, -192.0, 0.0, 2.0, 94.0, 0.0, 1.0),
11407 new NutationModel( 0, 0, 2,-3, 2, -188.0, 0.0, 0.0, 83.0, 0.0, 0.0),
11408
11409 /* 161-170 */
11410 new NutationModel(-1,-2, 0, 2, 0, 276.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11411 new NutationModel( 2, 1, 0, 0, 0, -286.0, 0.0, 1.0, 6.0, 0.0, 0.0),
11412 new NutationModel( 0, 0, 4, 0, 2, 186.0, 0.0, -1.0, -79.0, 0.0, 0.0),
11413 new NutationModel( 0, 0, 0, 0, 3, -219.0, 0.0, 0.0, 43.0, 0.0, 0.0),
11414 new NutationModel( 0, 3, 0, 0, 0, 276.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11415 new NutationModel( 0, 0, 2,-4, 1, -153.0, 0.0, -1.0, 84.0, 0.0, 0.0),
11416 new NutationModel( 0,-1, 0, 2, 1, -156.0, 0.0, 0.0, 81.0, 0.0, 0.0),
11417 new NutationModel( 0, 0, 0, 4, 1, -154.0, 0.0, 1.0, 78.0, 0.0, 0.0),
11418 new NutationModel(-1,-1, 2, 4, 2, -174.0, 0.0, 1.0, 75.0, 0.0, 0.0),
11419 new NutationModel( 1, 0, 2, 4, 2, -163.0, 0.0, 2.0, 69.0, 0.0, 1.0),
11420
11421 /* 171-180 */
11422 new NutationModel(-2, 2, 0, 2, 0, -228.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11423 new NutationModel(-2,-1, 2, 0, 1, 91.0, 0.0, -4.0, -54.0, 0.0, -2.0),
11424 new NutationModel(-2, 0, 0, 2, 2, 175.0, 0.0, 0.0, -75.0, 0.0, 0.0),
11425 new NutationModel(-1,-1, 2, 0, 2, -159.0, 0.0, 0.0, 69.0, 0.0, 0.0),
11426 new NutationModel( 0, 0, 4,-2, 1, 141.0, 0.0, 0.0, -72.0, 0.0, 0.0),
11427 new NutationModel( 3, 0, 2,-2, 1, 147.0, 0.0, 0.0, -75.0, 0.0, 0.0),
11428 new NutationModel(-2,-1, 0, 2, 1, -132.0, 0.0, 0.0, 69.0, 0.0, 0.0),
11429 new NutationModel( 1, 0, 0,-1, 1, 159.0, 0.0, -28.0, -54.0, 0.0, 11.0),
11430 new NutationModel( 0,-2, 0, 2, 0, 213.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11431 new NutationModel(-2, 0, 0, 4, 1, 123.0, 0.0, 0.0, -64.0, 0.0, 0.0),
11432
11433 /* 181-190 */
11434 new NutationModel(-3, 0, 0, 0, 1, -118.0, 0.0, -1.0, 66.0, 0.0, 0.0),
11435 new NutationModel( 1, 1, 2, 2, 2, 144.0, 0.0, -1.0, -61.0, 0.0, 0.0),
11436 new NutationModel( 0, 0, 2, 4, 1, -121.0, 0.0, 1.0, 60.0, 0.0, 0.0),
11437 new NutationModel( 3, 0, 2, 2, 2, -134.0, 0.0, 1.0, 56.0, 0.0, 1.0),
11438 new NutationModel(-1, 1, 2,-2, 1, -105.0, 0.0, 0.0, 57.0, 0.0, 0.0),
11439 new NutationModel( 2, 0, 0,-4, 1, -102.0, 0.0, 0.0, 56.0, 0.0, 0.0),
11440 new NutationModel( 0, 0, 0,-2, 2, 120.0, 0.0, 0.0, -52.0, 0.0, 0.0),
11441 new NutationModel( 2, 0, 2,-4, 1, 101.0, 0.0, 0.0, -54.0, 0.0, 0.0),
11442 new NutationModel(-1, 1, 0, 2, 1, -113.0, 0.0, 0.0, 59.0, 0.0, 0.0),
11443 new NutationModel( 0, 0, 2,-1, 1, -106.0, 0.0, 0.0, 61.0, 0.0, 0.0),
11444
11445 /* 191-200 */
11446 new NutationModel( 0,-2, 2, 2, 2, -129.0, 0.0, 1.0, 55.0, 0.0, 0.0),
11447 new NutationModel( 2, 0, 0, 2, 1, -114.0, 0.0, 0.0, 57.0, 0.0, 0.0),
11448 new NutationModel( 4, 0, 2,-2, 2, 113.0, 0.0, -1.0, -49.0, 0.0, 0.0),
11449 new NutationModel( 2, 0, 0,-2, 2, -102.0, 0.0, 0.0, 44.0, 0.0, 0.0),
11450 new NutationModel( 0, 2, 0, 0, 1, -94.0, 0.0, 0.0, 51.0, 0.0, 0.0),
11451 new NutationModel( 1, 0, 0,-4, 1, -100.0, 0.0, -1.0, 56.0, 0.0, 0.0),
11452 new NutationModel( 0, 2, 2,-2, 1, 87.0, 0.0, 0.0, -47.0, 0.0, 0.0),
11453 new NutationModel(-3, 0, 0, 4, 0, 161.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11454 new NutationModel(-1, 1, 2, 0, 1, 96.0, 0.0, 0.0, -50.0, 0.0, 0.0),
11455 new NutationModel(-1,-1, 0, 4, 0, 151.0, 0.0, -1.0, -5.0, 0.0, 0.0),
11456
11457 /* 201-210 */
11458 new NutationModel(-1,-2, 2, 2, 2, -104.0, 0.0, 0.0, 44.0, 0.0, 0.0),
11459 new NutationModel(-2,-1, 2, 4, 2, -110.0, 0.0, 0.0, 48.0, 0.0, 0.0),
11460 new NutationModel( 1,-1, 2, 2, 1, -100.0, 0.0, 1.0, 50.0, 0.0, 0.0),
11461 new NutationModel(-2, 1, 0, 2, 0, 92.0, 0.0, -5.0, 12.0, 0.0, -2.0),
11462 new NutationModel(-2, 1, 2, 0, 1, 82.0, 0.0, 0.0, -45.0, 0.0, 0.0),
11463 new NutationModel( 2, 1, 0,-2, 1, 82.0, 0.0, 0.0, -45.0, 0.0, 0.0),
11464 new NutationModel(-3, 0, 2, 0, 1, -78.0, 0.0, 0.0, 41.0, 0.0, 0.0),
11465 new NutationModel(-2, 0, 2,-2, 1, -77.0, 0.0, 0.0, 43.0, 0.0, 0.0),
11466 new NutationModel(-1, 1, 0, 2, 2, 2.0, 0.0, 0.0, 54.0, 0.0, 0.0),
11467 new NutationModel( 0,-1, 2,-1, 2, 94.0, 0.0, 0.0, -40.0, 0.0, 0.0),
11468
11469 /* 211-220 */
11470 new NutationModel(-1, 0, 4,-2, 2, -93.0, 0.0, 0.0, 40.0, 0.0, 0.0),
11471 new NutationModel( 0,-2, 2, 0, 2, -83.0, 0.0, 10.0, 40.0, 0.0, -2.0),
11472 new NutationModel(-1, 0, 2, 1, 2, 83.0, 0.0, 0.0, -36.0, 0.0, 0.0),
11473 new NutationModel( 2, 0, 0, 0, 2, -91.0, 0.0, 0.0, 39.0, 0.0, 0.0),
11474 new NutationModel( 0, 0, 2, 0, 3, 128.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11475 new NutationModel(-2, 0, 4, 0, 2, -79.0, 0.0, 0.0, 34.0, 0.0, 0.0),
11476 new NutationModel(-1, 0,-2, 0, 1, -83.0, 0.0, 0.0, 47.0, 0.0, 0.0),
11477 new NutationModel(-1, 1, 2, 2, 1, 84.0, 0.0, 0.0, -44.0, 0.0, 0.0),
11478 new NutationModel( 3, 0, 0, 0, 1, 83.0, 0.0, 0.0, -43.0, 0.0, 0.0),
11479 new NutationModel(-1, 0, 2, 3, 2, 91.0, 0.0, 0.0, -39.0, 0.0, 0.0),
11480
11481 /* 221-230 */
11482 new NutationModel( 2,-1, 2, 0, 1, -77.0, 0.0, 0.0, 39.0, 0.0, 0.0),
11483 new NutationModel( 0, 1, 2, 2, 1, 84.0, 0.0, 0.0, -43.0, 0.0, 0.0),
11484 new NutationModel( 0,-1, 2, 4, 2, -92.0, 0.0, 1.0, 39.0, 0.0, 0.0),
11485 new NutationModel( 2,-1, 2, 2, 2, -92.0, 0.0, 1.0, 39.0, 0.0, 0.0),
11486 new NutationModel( 0, 2,-2, 2, 0, -94.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11487 new NutationModel(-1,-1, 2,-1, 1, 68.0, 0.0, 0.0, -36.0, 0.0, 0.0),
11488 new NutationModel( 0,-2, 0, 0, 1, -61.0, 0.0, 0.0, 32.0, 0.0, 0.0),
11489 new NutationModel( 1, 0, 2,-4, 2, 71.0, 0.0, 0.0, -31.0, 0.0, 0.0),
11490 new NutationModel( 1,-1, 0,-2, 1, 62.0, 0.0, 0.0, -34.0, 0.0, 0.0),
11491 new NutationModel(-1,-1, 2, 0, 1, -63.0, 0.0, 0.0, 33.0, 0.0, 0.0),
11492
11493 /* 231-240 */
11494 new NutationModel( 1,-1, 2,-2, 2, -73.0, 0.0, 0.0, 32.0, 0.0, 0.0),
11495 new NutationModel(-2,-1, 0, 4, 0, 115.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11496 new NutationModel(-1, 0, 0, 3, 0, -103.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11497 new NutationModel(-2,-1, 2, 2, 2, 63.0, 0.0, 0.0, -28.0, 0.0, 0.0),
11498 new NutationModel( 0, 2, 2, 0, 2, 74.0, 0.0, 0.0, -32.0, 0.0, 0.0),
11499 new NutationModel( 1, 1, 0, 2, 0, -103.0, 0.0, -3.0, 3.0, 0.0, -1.0),
11500 new NutationModel( 2, 0, 2,-1, 2, -69.0, 0.0, 0.0, 30.0, 0.0, 0.0),
11501 new NutationModel( 1, 0, 2, 1, 1, 57.0, 0.0, 0.0, -29.0, 0.0, 0.0),
11502 new NutationModel( 4, 0, 0, 0, 0, 94.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11503 new NutationModel( 2, 1, 2, 0, 1, 64.0, 0.0, 0.0, -33.0, 0.0, 0.0),
11504
11505 /* 241-250 */
11506 new NutationModel( 3,-1, 2, 0, 2, -63.0, 0.0, 0.0, 26.0, 0.0, 0.0),
11507 new NutationModel(-2, 2, 0, 2, 1, -38.0, 0.0, 0.0, 20.0, 0.0, 0.0),
11508 new NutationModel( 1, 0, 2,-3, 1, -43.0, 0.0, 0.0, 24.0, 0.0, 0.0),
11509 new NutationModel( 1, 1, 2,-4, 1, -45.0, 0.0, 0.0, 23.0, 0.0, 0.0),
11510 new NutationModel(-1,-1, 2,-2, 1, 47.0, 0.0, 0.0, -24.0, 0.0, 0.0),
11511 new NutationModel( 0,-1, 0,-1, 1, -48.0, 0.0, 0.0, 25.0, 0.0, 0.0),
11512 new NutationModel( 0,-1, 0,-2, 1, 45.0, 0.0, 0.0, -26.0, 0.0, 0.0),
11513 new NutationModel(-2, 0, 0, 0, 2, 56.0, 0.0, 0.0, -25.0, 0.0, 0.0),
11514 new NutationModel(-2, 0,-2, 2, 0, 88.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11515 new NutationModel(-1, 0,-2, 4, 0, -75.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11516
11517 /* 251-260 */
11518 new NutationModel( 1,-2, 0, 0, 0, 85.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11519 new NutationModel( 0, 1, 0, 1, 1, 49.0, 0.0, 0.0, -26.0, 0.0, 0.0),
11520 new NutationModel(-1, 2, 0, 2, 0, -74.0, 0.0, -3.0, -1.0, 0.0, -1.0),
11521 new NutationModel( 1,-1, 2,-2, 1, -39.0, 0.0, 0.0, 21.0, 0.0, 0.0),
11522 new NutationModel( 1, 2, 2,-2, 2, 45.0, 0.0, 0.0, -20.0, 0.0, 0.0),
11523 new NutationModel( 2,-1, 2,-2, 2, 51.0, 0.0, 0.0, -22.0, 0.0, 0.0),
11524 new NutationModel( 1, 0, 2,-1, 1, -40.0, 0.0, 0.0, 21.0, 0.0, 0.0),
11525 new NutationModel( 2, 1, 2,-2, 1, 41.0, 0.0, 0.0, -21.0, 0.0, 0.0),
11526 new NutationModel(-2, 0, 0,-2, 1, -42.0, 0.0, 0.0, 24.0, 0.0, 0.0),
11527 new NutationModel( 1,-2, 2, 0, 2, -51.0, 0.0, 0.0, 22.0, 0.0, 0.0),
11528
11529 /* 261-270 */
11530 new NutationModel( 0, 1, 2, 1, 1, -42.0, 0.0, 0.0, 22.0, 0.0, 0.0),
11531 new NutationModel( 1, 0, 4,-2, 1, 39.0, 0.0, 0.0, -21.0, 0.0, 0.0),
11532 new NutationModel(-2, 0, 4, 2, 2, 46.0, 0.0, 0.0, -18.0, 0.0, 0.0),
11533 new NutationModel( 1, 1, 2, 1, 2, -53.0, 0.0, 0.0, 22.0, 0.0, 0.0),
11534 new NutationModel( 1, 0, 0, 4, 0, 82.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11535 new NutationModel( 1, 0, 2, 2, 0, 81.0, 0.0, -1.0, -4.0, 0.0, 0.0),
11536 new NutationModel( 2, 0, 2, 1, 2, 47.0, 0.0, 0.0, -19.0, 0.0, 0.0),
11537 new NutationModel( 3, 1, 2, 0, 2, 53.0, 0.0, 0.0, -23.0, 0.0, 0.0),
11538 new NutationModel( 4, 0, 2, 0, 1, -45.0, 0.0, 0.0, 22.0, 0.0, 0.0),
11539 new NutationModel(-2,-1, 2, 0, 0, -44.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11540
11541 /* 271-280 */
11542 new NutationModel( 0, 1,-2, 2, 1, -33.0, 0.0, 0.0, 16.0, 0.0, 0.0),
11543 new NutationModel( 1, 0,-2, 1, 0, -61.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11544 new NutationModel( 0,-1,-2, 2, 1, 28.0, 0.0, 0.0, -15.0, 0.0, 0.0),
11545 new NutationModel( 2,-1, 0,-2, 1, -38.0, 0.0, 0.0, 19.0, 0.0, 0.0),
11546 new NutationModel(-1, 0, 2,-1, 2, -33.0, 0.0, 0.0, 21.0, 0.0, 0.0),
11547 new NutationModel( 1, 0, 2,-3, 2, -60.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11548 new NutationModel( 0, 1, 2,-2, 3, 48.0, 0.0, 0.0, -10.0, 0.0, 0.0),
11549 new NutationModel( 0, 0, 2,-3, 1, 27.0, 0.0, 0.0, -14.0, 0.0, 0.0),
11550 new NutationModel(-1, 0,-2, 2, 1, 38.0, 0.0, 0.0, -20.0, 0.0, 0.0),
11551 new NutationModel( 0, 0, 2,-4, 2, 31.0, 0.0, 0.0, -13.0, 0.0, 0.0),
11552
11553 /* 281-290 */
11554 new NutationModel(-2, 1, 0, 0, 1, -29.0, 0.0, 0.0, 15.0, 0.0, 0.0),
11555 new NutationModel(-1, 0, 0,-1, 1, 28.0, 0.0, 0.0, -15.0, 0.0, 0.0),
11556 new NutationModel( 2, 0, 2,-4, 2, -32.0, 0.0, 0.0, 15.0, 0.0, 0.0),
11557 new NutationModel( 0, 0, 4,-4, 4, 45.0, 0.0, 0.0, -8.0, 0.0, 0.0),
11558 new NutationModel( 0, 0, 4,-4, 2, -44.0, 0.0, 0.0, 19.0, 0.0, 0.0),
11559 new NutationModel(-1,-2, 0, 2, 1, 28.0, 0.0, 0.0, -15.0, 0.0, 0.0),
11560 new NutationModel(-2, 0, 0, 3, 0, -51.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11561 new NutationModel( 1, 0,-2, 2, 1, -36.0, 0.0, 0.0, 20.0, 0.0, 0.0),
11562 new NutationModel(-3, 0, 2, 2, 2, 44.0, 0.0, 0.0, -19.0, 0.0, 0.0),
11563 new NutationModel(-3, 0, 2, 2, 1, 26.0, 0.0, 0.0, -14.0, 0.0, 0.0),
11564
11565 /* 291-300 */
11566 new NutationModel(-2, 0, 2, 2, 0, -60.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11567 new NutationModel( 2,-1, 0, 0, 1, 35.0, 0.0, 0.0, -18.0, 0.0, 0.0),
11568 new NutationModel(-2, 1, 2, 2, 2, -27.0, 0.0, 0.0, 11.0, 0.0, 0.0),
11569 new NutationModel( 1, 1, 0, 1, 0, 47.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11570 new NutationModel( 0, 1, 4,-2, 2, 36.0, 0.0, 0.0, -15.0, 0.0, 0.0),
11571 new NutationModel(-1, 1, 0,-2, 1, -36.0, 0.0, 0.0, 20.0, 0.0, 0.0),
11572 new NutationModel( 0, 0, 0,-4, 1, -35.0, 0.0, 0.0, 19.0, 0.0, 0.0),
11573 new NutationModel( 1,-1, 0, 2, 1, -37.0, 0.0, 0.0, 19.0, 0.0, 0.0),
11574 new NutationModel( 1, 1, 0, 2, 1, 32.0, 0.0, 0.0, -16.0, 0.0, 0.0),
11575 new NutationModel(-1, 2, 2, 2, 2, 35.0, 0.0, 0.0, -14.0, 0.0, 0.0),
11576
11577 /* 301-310 */
11578 new NutationModel( 3, 1, 2,-2, 2, 32.0, 0.0, 0.0, -13.0, 0.0, 0.0),
11579 new NutationModel( 0,-1, 0, 4, 0, 65.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11580 new NutationModel( 2,-1, 0, 2, 0, 47.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11581 new NutationModel( 0, 0, 4, 0, 1, 32.0, 0.0, 0.0, -16.0, 0.0, 0.0),
11582 new NutationModel( 2, 0, 4,-2, 2, 37.0, 0.0, 0.0, -16.0, 0.0, 0.0),
11583 new NutationModel(-1,-1, 2, 4, 1, -30.0, 0.0, 0.0, 15.0, 0.0, 0.0),
11584 new NutationModel( 1, 0, 0, 4, 1, -32.0, 0.0, 0.0, 16.0, 0.0, 0.0),
11585 new NutationModel( 1,-2, 2, 2, 2, -31.0, 0.0, 0.0, 13.0, 0.0, 0.0),
11586 new NutationModel( 0, 0, 2, 3, 2, 37.0, 0.0, 0.0, -16.0, 0.0, 0.0),
11587 new NutationModel(-1, 1, 2, 4, 2, 31.0, 0.0, 0.0, -13.0, 0.0, 0.0),
11588
11589 /* 311-320 */
11590 new NutationModel( 3, 0, 0, 2, 0, 49.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11591 new NutationModel(-1, 0, 4, 2, 2, 32.0, 0.0, 0.0, -13.0, 0.0, 0.0),
11592 new NutationModel( 1, 1, 2, 2, 1, 23.0, 0.0, 0.0, -12.0, 0.0, 0.0),
11593 new NutationModel(-2, 0, 2, 6, 2, -43.0, 0.0, 0.0, 18.0, 0.0, 0.0),
11594 new NutationModel( 2, 1, 2, 2, 2, 26.0, 0.0, 0.0, -11.0, 0.0, 0.0),
11595 new NutationModel(-1, 0, 2, 6, 2, -32.0, 0.0, 0.0, 14.0, 0.0, 0.0),
11596 new NutationModel( 1, 0, 2, 4, 1, -29.0, 0.0, 0.0, 14.0, 0.0, 0.0),
11597 new NutationModel( 2, 0, 2, 4, 2, -27.0, 0.0, 0.0, 12.0, 0.0, 0.0),
11598 new NutationModel( 1, 1,-2, 1, 0, 30.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11599 new NutationModel(-3, 1, 2, 1, 2, -11.0, 0.0, 0.0, 5.0, 0.0, 0.0),
11600
11601 /* 321-330 */
11602 new NutationModel( 2, 0,-2, 0, 2, -21.0, 0.0, 0.0, 10.0, 0.0, 0.0),
11603 new NutationModel(-1, 0, 0, 1, 2, -34.0, 0.0, 0.0, 15.0, 0.0, 0.0),
11604 new NutationModel(-4, 0, 2, 2, 1, -10.0, 0.0, 0.0, 6.0, 0.0, 0.0),
11605 new NutationModel(-1,-1, 0, 1, 0, -36.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11606 new NutationModel( 0, 0,-2, 2, 2, -9.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11607 new NutationModel( 1, 0, 0,-1, 2, -12.0, 0.0, 0.0, 5.0, 0.0, 0.0),
11608 new NutationModel( 0,-1, 2,-2, 3, -21.0, 0.0, 0.0, 5.0, 0.0, 0.0),
11609 new NutationModel(-2, 1, 2, 0, 0, -29.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11610 new NutationModel( 0, 0, 2,-2, 4, -15.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11611 new NutationModel(-2,-2, 0, 2, 0, -20.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11612
11613 /* 331-340 */
11614 new NutationModel(-2, 0,-2, 4, 0, 28.0, 0.0, 0.0, 0.0, 0.0, -2.0),
11615 new NutationModel( 0,-2,-2, 2, 0, 17.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11616 new NutationModel( 1, 2, 0,-2, 1, -22.0, 0.0, 0.0, 12.0, 0.0, 0.0),
11617 new NutationModel( 3, 0, 0,-4, 1, -14.0, 0.0, 0.0, 7.0, 0.0, 0.0),
11618 new NutationModel(-1, 1, 2,-2, 2, 24.0, 0.0, 0.0, -11.0, 0.0, 0.0),
11619 new NutationModel( 1,-1, 2,-4, 1, 11.0, 0.0, 0.0, -6.0, 0.0, 0.0),
11620 new NutationModel( 1, 1, 0,-2, 2, 14.0, 0.0, 0.0, -6.0, 0.0, 0.0),
11621 new NutationModel(-3, 0, 2, 0, 0, 24.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11622 new NutationModel(-3, 0, 2, 0, 2, 18.0, 0.0, 0.0, -8.0, 0.0, 0.0),
11623 new NutationModel(-2, 0, 0, 1, 0, -38.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11624
11625 /* 341-350 */
11626 new NutationModel( 0, 0,-2, 1, 0, -31.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11627 new NutationModel(-3, 0, 0, 2, 1, -16.0, 0.0, 0.0, 8.0, 0.0, 0.0),
11628 new NutationModel(-1,-1,-2, 2, 0, 29.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11629 new NutationModel( 0, 1, 2,-4, 1, -18.0, 0.0, 0.0, 10.0, 0.0, 0.0),
11630 new NutationModel( 2, 1, 0,-4, 1, -10.0, 0.0, 0.0, 5.0, 0.0, 0.0),
11631 new NutationModel( 0, 2, 0,-2, 1, -17.0, 0.0, 0.0, 10.0, 0.0, 0.0),
11632 new NutationModel( 1, 0, 0,-3, 1, 9.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11633 new NutationModel(-2, 0, 2,-2, 2, 16.0, 0.0, 0.0, -6.0, 0.0, 0.0),
11634 new NutationModel(-2,-1, 0, 0, 1, 22.0, 0.0, 0.0, -12.0, 0.0, 0.0),
11635 new NutationModel(-4, 0, 0, 2, 0, 20.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11636
11637 /* 351-360 */
11638 new NutationModel( 1, 1, 0,-4, 1, -13.0, 0.0, 0.0, 6.0, 0.0, 0.0),
11639 new NutationModel(-1, 0, 2,-4, 1, -17.0, 0.0, 0.0, 9.0, 0.0, 0.0),
11640 new NutationModel( 0, 0, 4,-4, 1, -14.0, 0.0, 0.0, 8.0, 0.0, 0.0),
11641 new NutationModel( 0, 3, 2,-2, 2, 0.0, 0.0, 0.0, -7.0, 0.0, 0.0),
11642 new NutationModel(-3,-1, 0, 4, 0, 14.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11643 new NutationModel(-3, 0, 0, 4, 1, 19.0, 0.0, 0.0, -10.0, 0.0, 0.0),
11644 new NutationModel( 1,-1,-2, 2, 0, -34.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11645 new NutationModel(-1,-1, 0, 2, 2, -20.0, 0.0, 0.0, 8.0, 0.0, 0.0),
11646 new NutationModel( 1,-2, 0, 0, 1, 9.0, 0.0, 0.0, -5.0, 0.0, 0.0),
11647 new NutationModel( 1,-1, 0, 0, 2, -18.0, 0.0, 0.0, 7.0, 0.0, 0.0),
11648
11649 /* 361-370 */
11650 new NutationModel( 0, 0, 0, 1, 2, 13.0, 0.0, 0.0, -6.0, 0.0, 0.0),
11651 new NutationModel(-1,-1, 2, 0, 0, 17.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11652 new NutationModel( 1,-2, 2,-2, 2, -12.0, 0.0, 0.0, 5.0, 0.0, 0.0),
11653 new NutationModel( 0,-1, 2,-1, 1, 15.0, 0.0, 0.0, -8.0, 0.0, 0.0),
11654 new NutationModel(-1, 0, 2, 0, 3, -11.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11655 new NutationModel( 1, 1, 0, 0, 2, 13.0, 0.0, 0.0, -5.0, 0.0, 0.0),
11656 new NutationModel(-1, 1, 2, 0, 0, -18.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11657 new NutationModel( 1, 2, 0, 0, 0, -35.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11658 new NutationModel(-1, 2, 2, 0, 2, 9.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11659 new NutationModel(-1, 0, 4,-2, 1, -19.0, 0.0, 0.0, 10.0, 0.0, 0.0),
11660
11661 /* 371-380 */
11662 new NutationModel( 3, 0, 2,-4, 2, -26.0, 0.0, 0.0, 11.0, 0.0, 0.0),
11663 new NutationModel( 1, 2, 2,-2, 1, 8.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11664 new NutationModel( 1, 0, 4,-4, 2, -10.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11665 new NutationModel(-2,-1, 0, 4, 1, 10.0, 0.0, 0.0, -6.0, 0.0, 0.0),
11666 new NutationModel( 0,-1, 0, 2, 2, -21.0, 0.0, 0.0, 9.0, 0.0, 0.0),
11667 new NutationModel(-2, 1, 0, 4, 0, -15.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11668 new NutationModel(-2,-1, 2, 2, 1, 9.0, 0.0, 0.0, -5.0, 0.0, 0.0),
11669 new NutationModel( 2, 0,-2, 2, 0, -29.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11670 new NutationModel( 1, 0, 0, 1, 1, -19.0, 0.0, 0.0, 10.0, 0.0, 0.0),
11671 new NutationModel( 0, 1, 0, 2, 2, 12.0, 0.0, 0.0, -5.0, 0.0, 0.0),
11672
11673 /* 381-390 */
11674 new NutationModel( 1,-1, 2,-1, 2, 22.0, 0.0, 0.0, -9.0, 0.0, 0.0),
11675 new NutationModel(-2, 0, 4, 0, 1, -10.0, 0.0, 0.0, 5.0, 0.0, 0.0),
11676 new NutationModel( 2, 1, 0, 0, 1, -20.0, 0.0, 0.0, 11.0, 0.0, 0.0),
11677 new NutationModel( 0, 1, 2, 0, 0, -20.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11678 new NutationModel( 0,-1, 4,-2, 2, -17.0, 0.0, 0.0, 7.0, 0.0, 0.0),
11679 new NutationModel( 0, 0, 4,-2, 4, 15.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11680 new NutationModel( 0, 2, 2, 0, 1, 8.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11681 new NutationModel(-3, 0, 0, 6, 0, 14.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11682 new NutationModel(-1,-1, 0, 4, 1, -12.0, 0.0, 0.0, 6.0, 0.0, 0.0),
11683 new NutationModel( 1,-2, 0, 2, 0, 25.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11684
11685 /* 391-400 */
11686 new NutationModel(-1, 0, 0, 4, 2, -13.0, 0.0, 0.0, 6.0, 0.0, 0.0),
11687 new NutationModel(-1,-2, 2, 2, 1, -14.0, 0.0, 0.0, 8.0, 0.0, 0.0),
11688 new NutationModel(-1, 0, 0,-2, 2, 13.0, 0.0, 0.0, -5.0, 0.0, 0.0),
11689 new NutationModel( 1, 0,-2,-2, 1, -17.0, 0.0, 0.0, 9.0, 0.0, 0.0),
11690 new NutationModel( 0, 0,-2,-2, 1, -12.0, 0.0, 0.0, 6.0, 0.0, 0.0),
11691 new NutationModel(-2, 0,-2, 0, 1, -10.0, 0.0, 0.0, 5.0, 0.0, 0.0),
11692 new NutationModel( 0, 0, 0, 3, 1, 10.0, 0.0, 0.0, -6.0, 0.0, 0.0),
11693 new NutationModel( 0, 0, 0, 3, 0, -15.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11694 new NutationModel(-1, 1, 0, 4, 0, -22.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11695 new NutationModel(-1,-1, 2, 2, 0, 28.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11696
11697 /* 401-410 */
11698 new NutationModel(-2, 0, 2, 3, 2, 15.0, 0.0, 0.0, -7.0, 0.0, 0.0),
11699 new NutationModel( 1, 0, 0, 2, 2, 23.0, 0.0, 0.0, -10.0, 0.0, 0.0),
11700 new NutationModel( 0,-1, 2, 1, 2, 12.0, 0.0, 0.0, -5.0, 0.0, 0.0),
11701 new NutationModel( 3,-1, 0, 0, 0, 29.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11702 new NutationModel( 2, 0, 0, 1, 0, -25.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11703 new NutationModel( 1,-1, 2, 0, 0, 22.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11704 new NutationModel( 0, 0, 2, 1, 0, -18.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11705 new NutationModel( 1, 0, 2, 0, 3, 15.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11706 new NutationModel( 3, 1, 0, 0, 0, -23.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11707 new NutationModel( 3,-1, 2,-2, 2, 12.0, 0.0, 0.0, -5.0, 0.0, 0.0),
11708
11709 /* 411-420 */
11710 new NutationModel( 2, 0, 2,-1, 1, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11711 new NutationModel( 1, 1, 2, 0, 0, -19.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11712 new NutationModel( 0, 0, 4,-1, 2, -10.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11713 new NutationModel( 1, 2, 2, 0, 2, 21.0, 0.0, 0.0, -9.0, 0.0, 0.0),
11714 new NutationModel(-2, 0, 0, 6, 0, 23.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11715 new NutationModel( 0,-1, 0, 4, 1, -16.0, 0.0, 0.0, 8.0, 0.0, 0.0),
11716 new NutationModel(-2,-1, 2, 4, 1, -19.0, 0.0, 0.0, 9.0, 0.0, 0.0),
11717 new NutationModel( 0,-2, 2, 2, 1, -22.0, 0.0, 0.0, 10.0, 0.0, 0.0),
11718 new NutationModel( 0,-1, 2, 2, 0, 27.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11719 new NutationModel(-1, 0, 2, 3, 1, 16.0, 0.0, 0.0, -8.0, 0.0, 0.0),
11720
11721 /* 421-430 */
11722 new NutationModel(-2, 1, 2, 4, 2, 19.0, 0.0, 0.0, -8.0, 0.0, 0.0),
11723 new NutationModel( 2, 0, 0, 2, 2, 9.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11724 new NutationModel( 2,-2, 2, 0, 2, -9.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11725 new NutationModel(-1, 1, 2, 3, 2, -9.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11726 new NutationModel( 3, 0, 2,-1, 2, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11727 new NutationModel( 4, 0, 2,-2, 1, 18.0, 0.0, 0.0, -9.0, 0.0, 0.0),
11728 new NutationModel(-1, 0, 0, 6, 0, 16.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11729 new NutationModel(-1,-2, 2, 4, 2, -10.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11730 new NutationModel(-3, 0, 2, 6, 2, -23.0, 0.0, 0.0, 9.0, 0.0, 0.0),
11731 new NutationModel(-1, 0, 2, 4, 0, 16.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11732
11733 /* 431-440 */
11734 new NutationModel( 3, 0, 0, 2, 1, -12.0, 0.0, 0.0, 6.0, 0.0, 0.0),
11735 new NutationModel( 3,-1, 2, 0, 1, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11736 new NutationModel( 3, 0, 2, 0, 0, 30.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11737 new NutationModel( 1, 0, 4, 0, 2, 24.0, 0.0, 0.0, -10.0, 0.0, 0.0),
11738 new NutationModel( 5, 0, 2,-2, 2, 10.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11739 new NutationModel( 0,-1, 2, 4, 1, -16.0, 0.0, 0.0, 7.0, 0.0, 0.0),
11740 new NutationModel( 2,-1, 2, 2, 1, -16.0, 0.0, 0.0, 7.0, 0.0, 0.0),
11741 new NutationModel( 0, 1, 2, 4, 2, 17.0, 0.0, 0.0, -7.0, 0.0, 0.0),
11742 new NutationModel( 1,-1, 2, 4, 2, -24.0, 0.0, 0.0, 10.0, 0.0, 0.0),
11743 new NutationModel( 3,-1, 2, 2, 2, -12.0, 0.0, 0.0, 5.0, 0.0, 0.0),
11744
11745 /* 441-450 */
11746 new NutationModel( 3, 0, 2, 2, 1, -24.0, 0.0, 0.0, 11.0, 0.0, 0.0),
11747 new NutationModel( 5, 0, 2, 0, 2, -23.0, 0.0, 0.0, 9.0, 0.0, 0.0),
11748 new NutationModel( 0, 0, 2, 6, 2, -13.0, 0.0, 0.0, 5.0, 0.0, 0.0),
11749 new NutationModel( 4, 0, 2, 2, 2, -15.0, 0.0, 0.0, 7.0, 0.0, 0.0),
11750 new NutationModel( 0,-1, 1,-1, 1, 0.0, 0.0,-1988.0, 0.0, 0.0,-1679.0),
11751 new NutationModel(-1, 0, 1, 0, 3, 0.0, 0.0, -63.0, 0.0, 0.0, -27.0),
11752 new NutationModel( 0,-2, 2,-2, 3, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11753 new NutationModel( 1, 0,-1, 0, 1, 0.0, 0.0, 5.0, 0.0, 0.0, 4.0),
11754 new NutationModel( 2,-2, 0,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11755 new NutationModel(-1, 0, 1, 0, 2, 0.0, 0.0, 364.0, 0.0, 0.0, 176.0),
11756
11757 /* 451-460 */
11758 new NutationModel(-1, 0, 1, 0, 1, 0.0, 0.0,-1044.0, 0.0, 0.0, -891.0),
11759 new NutationModel(-1,-1, 2,-1, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11760 new NutationModel(-2, 2, 0, 2, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11761 new NutationModel(-1, 0, 1, 0, 0, 0.0, 0.0, 330.0, 0.0, 0.0, 0.0),
11762 new NutationModel(-4, 1, 2, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11763 new NutationModel(-3, 0, 2, 1, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11764 new NutationModel(-2,-1, 2, 0, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11765 new NutationModel( 1, 0,-2, 1, 1, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11766 new NutationModel( 2,-1,-2, 0, 1, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11767 new NutationModel(-4, 0, 2, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11768
11769 /* 461-470 */
11770 new NutationModel(-3, 1, 0, 3, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11771 new NutationModel(-1, 0,-1, 2, 0, 0.0, 0.0, 5.0, 0.0, 0.0, 0.0),
11772 new NutationModel( 0,-2, 0, 0, 2, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11773 new NutationModel( 0,-2, 0, 0, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11774 new NutationModel(-3, 0, 0, 3, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11775 new NutationModel(-2,-1, 0, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11776 new NutationModel(-1, 0,-2, 3, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11777 new NutationModel(-4, 0, 0, 4, 0, -12.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11778 new NutationModel( 2, 1,-2, 0, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11779 new NutationModel( 2,-1, 0,-2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11780
11781 /* 471-480 */
11782 new NutationModel( 0, 0, 1,-1, 0, -5.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11783 new NutationModel(-1, 2, 0, 1, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11784 new NutationModel(-2, 1, 2, 0, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11785 new NutationModel( 1, 1, 0,-1, 1, 7.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11786 new NutationModel( 1, 0, 1,-2, 1, 0.0, 0.0, -12.0, 0.0, 0.0, -10.0),
11787 new NutationModel( 0, 2, 0, 0, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11788 new NutationModel( 1,-1, 2,-3, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11789 new NutationModel(-1, 1, 2,-1, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11790 new NutationModel(-2, 0, 4,-2, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11791 new NutationModel(-2, 0, 4,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11792
11793 /* 481-490 */
11794 new NutationModel(-2,-2, 0, 2, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11795 new NutationModel(-2, 0,-2, 4, 0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11796 new NutationModel( 1, 2, 2,-4, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11797 new NutationModel( 1, 1, 2,-4, 2, 7.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11798 new NutationModel(-1, 2, 2,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11799 new NutationModel( 2, 0, 0,-3, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11800 new NutationModel(-1, 2, 0, 0, 1, -5.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11801 new NutationModel( 0, 0, 0,-2, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11802 new NutationModel(-1,-1, 2,-2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11803 new NutationModel(-1, 1, 0, 0, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11804
11805 /* 491-500 */
11806 new NutationModel( 0, 0, 0,-1, 2, -8.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11807 new NutationModel(-2, 1, 0, 1, 0, 9.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11808 new NutationModel( 1,-2, 0,-2, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11809 new NutationModel( 1, 0,-2, 0, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11810 new NutationModel(-3, 1, 0, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11811 new NutationModel(-1, 1,-2, 2, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11812 new NutationModel(-1,-1, 0, 0, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11813 new NutationModel(-3, 0, 0, 2, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11814 new NutationModel(-3,-1, 0, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11815 new NutationModel( 2, 0, 2,-6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11816
11817 /* 501-510 */
11818 new NutationModel( 0, 1, 2,-4, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11819 new NutationModel( 2, 0, 0,-4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11820 new NutationModel(-2, 1, 2,-2, 1, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11821 new NutationModel( 0,-1, 2,-4, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11822 new NutationModel( 0, 1, 0,-2, 2, 9.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11823 new NutationModel(-1, 0, 0,-2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11824 new NutationModel( 2, 0,-2,-2, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11825 new NutationModel(-4, 0, 2, 0, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11826 new NutationModel(-1,-1, 0,-1, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11827 new NutationModel( 0, 0,-2, 0, 2, 9.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11828
11829 /* 511-520 */
11830 new NutationModel(-3, 0, 0, 1, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11831 new NutationModel(-1, 0,-2, 1, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11832 new NutationModel(-2, 0,-2, 2, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11833 new NutationModel( 0, 0,-4, 2, 0, 8.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11834 new NutationModel(-2,-1,-2, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11835 new NutationModel( 1, 0, 2,-6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11836 new NutationModel(-1, 0, 2,-4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11837 new NutationModel( 1, 0, 0,-4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11838 new NutationModel( 2, 1, 2,-4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11839 new NutationModel( 2, 1, 2,-4, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11840
11841 /* 521-530 */
11842 new NutationModel( 0, 1, 4,-4, 4, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11843 new NutationModel( 0, 1, 4,-4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11844 new NutationModel(-1,-1,-2, 4, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11845 new NutationModel(-1,-3, 0, 2, 0, 9.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11846 new NutationModel(-1, 0,-2, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11847 new NutationModel(-2,-1, 0, 3, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11848 new NutationModel( 0, 0,-2, 3, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11849 new NutationModel(-2, 0, 0, 3, 1, -5.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11850 new NutationModel( 0,-1, 0, 1, 0, -13.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11851 new NutationModel(-3, 0, 2, 2, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11852
11853 /* 531-540 */
11854 new NutationModel( 1, 1,-2, 2, 0, 10.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11855 new NutationModel(-1, 1, 0, 2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11856 new NutationModel( 1,-2, 2,-2, 1, 10.0, 0.0, 13.0, 6.0, 0.0, -5.0),
11857 new NutationModel( 0, 0, 1, 0, 2, 0.0, 0.0, 30.0, 0.0, 0.0, 14.0),
11858 new NutationModel( 0, 0, 1, 0, 1, 0.0, 0.0, -162.0, 0.0, 0.0, -138.0),
11859 new NutationModel( 0, 0, 1, 0, 0, 0.0, 0.0, 75.0, 0.0, 0.0, 0.0),
11860 new NutationModel(-1, 2, 0, 2, 1, -7.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11861 new NutationModel( 0, 0, 2, 0, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11862 new NutationModel(-2, 0, 2, 0, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11863 new NutationModel( 2, 0, 0,-1, 1, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11864
11865 /* 541-550 */
11866 new NutationModel( 3, 0, 0,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11867 new NutationModel( 1, 0, 2,-2, 3, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11868 new NutationModel( 1, 2, 0, 0, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11869 new NutationModel( 2, 0, 2,-3, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11870 new NutationModel(-1, 1, 4,-2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11871 new NutationModel(-2,-2, 0, 4, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11872 new NutationModel( 0,-3, 0, 2, 0, 9.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11873 new NutationModel( 0, 0,-2, 4, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11874 new NutationModel(-1,-1, 0, 3, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11875 new NutationModel(-2, 0, 0, 4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11876
11877 /* 551-560 */
11878 new NutationModel(-1, 0, 0, 3, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11879 new NutationModel( 2,-2, 0, 0, 0, 7.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11880 new NutationModel( 1,-1, 0, 1, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11881 new NutationModel(-1, 0, 0, 2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11882 new NutationModel( 0,-2, 2, 0, 1, -6.0, 0.0, -3.0, 3.0, 0.0, 1.0),
11883 new NutationModel(-1, 0, 1, 2, 1, 0.0, 0.0, -3.0, 0.0, 0.0, -2.0),
11884 new NutationModel(-1, 1, 0, 3, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11885 new NutationModel(-1,-1, 2, 1, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11886 new NutationModel( 0,-1, 2, 0, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11887 new NutationModel(-2, 1, 2, 2, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11888
11889 /* 561-570 */
11890 new NutationModel( 2,-2, 2,-2, 2, -1.0, 0.0, 3.0, 3.0, 0.0, -1.0),
11891 new NutationModel( 1, 1, 0, 1, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11892 new NutationModel( 1, 0, 1, 0, 1, 0.0, 0.0, -13.0, 0.0, 0.0, -11.0),
11893 new NutationModel( 1, 0, 1, 0, 0, 3.0, 0.0, 6.0, 0.0, 0.0, 0.0),
11894 new NutationModel( 0, 2, 0, 2, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11895 new NutationModel( 2,-1, 2,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11896 new NutationModel( 0,-1, 4,-2, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11897 new NutationModel( 0, 0, 4,-2, 3, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11898 new NutationModel( 0, 1, 4,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11899 new NutationModel( 4, 0, 2,-4, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11900
11901 /* 571-580 */
11902 new NutationModel( 2, 2, 2,-2, 2, 8.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11903 new NutationModel( 2, 0, 4,-4, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11904 new NutationModel(-1,-2, 0, 4, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11905 new NutationModel(-1,-3, 2, 2, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11906 new NutationModel(-3, 0, 2, 4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11907 new NutationModel(-3, 0, 2,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11908 new NutationModel(-1,-1, 0,-2, 1, 8.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11909 new NutationModel(-3, 0, 0, 0, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11910 new NutationModel(-3, 0,-2, 2, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11911 new NutationModel( 0, 1, 0,-4, 1, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11912
11913 /* 581-590 */
11914 new NutationModel(-2, 1, 0,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11915 new NutationModel(-4, 0, 0, 0, 1, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11916 new NutationModel(-1, 0, 0,-4, 1, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11917 new NutationModel(-3, 0, 0,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11918 new NutationModel( 0, 0, 0, 3, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11919 new NutationModel(-1, 1, 0, 4, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11920 new NutationModel( 1,-2, 2, 0, 1, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11921 new NutationModel( 0, 1, 0, 3, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11922 new NutationModel(-1, 0, 2, 2, 3, 6.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11923 new NutationModel( 0, 0, 2, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11924
11925 /* 591-600 */
11926 new NutationModel(-2, 0, 2, 2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11927 new NutationModel(-1, 1, 2, 2, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11928 new NutationModel( 3, 0, 0, 0, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11929 new NutationModel( 2, 1, 0, 1, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11930 new NutationModel( 2,-1, 2,-1, 2, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11931 new NutationModel( 0, 0, 2, 0, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11932 new NutationModel( 0, 0, 3, 0, 3, 0.0, 0.0, -26.0, 0.0, 0.0, -11.0),
11933 new NutationModel( 0, 0, 3, 0, 2, 0.0, 0.0, -10.0, 0.0, 0.0, -5.0),
11934 new NutationModel(-1, 2, 2, 2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11935 new NutationModel(-1, 0, 4, 0, 0, -13.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11936
11937 /* 601-610 */
11938 new NutationModel( 1, 2, 2, 0, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11939 new NutationModel( 3, 1, 2,-2, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11940 new NutationModel( 1, 1, 4,-2, 2, 7.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11941 new NutationModel(-2,-1, 0, 6, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11942 new NutationModel( 0,-2, 0, 4, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11943 new NutationModel(-2, 0, 0, 6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11944 new NutationModel(-2,-2, 2, 4, 2, -6.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11945 new NutationModel( 0,-3, 2, 2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11946 new NutationModel( 0, 0, 0, 4, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11947 new NutationModel(-1,-1, 2, 3, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11948
11949 /* 611-620 */
11950 new NutationModel(-2, 0, 2, 4, 0, 13.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11951 new NutationModel( 2,-1, 0, 2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11952 new NutationModel( 1, 0, 0, 3, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11953 new NutationModel( 0, 1, 0, 4, 1, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11954 new NutationModel( 0, 1, 0, 4, 0, -11.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11955 new NutationModel( 1,-1, 2, 1, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11956 new NutationModel( 0, 0, 2, 2, 3, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11957 new NutationModel( 1, 0, 2, 2, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11958 new NutationModel(-1, 0, 2, 2, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11959 new NutationModel(-2, 0, 4, 2, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11960
11961 /* 621-630 */
11962 new NutationModel( 2, 1, 0, 2, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11963 new NutationModel( 2, 1, 0, 2, 0, -12.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11964 new NutationModel( 2,-1, 2, 0, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11965 new NutationModel( 1, 0, 2, 1, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11966 new NutationModel( 0, 1, 2, 2, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11967 new NutationModel( 2, 0, 2, 0, 3, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11968 new NutationModel( 3, 0, 2, 0, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11969 new NutationModel( 1, 0, 2, 0, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11970 new NutationModel( 1, 0, 3, 0, 3, 0.0, 0.0, -5.0, 0.0, 0.0, -2.0),
11971 new NutationModel( 1, 1, 2, 1, 1, -7.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11972
11973 /* 631-640 */
11974 new NutationModel( 0, 2, 2, 2, 2, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11975 new NutationModel( 2, 1, 2, 0, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11976 new NutationModel( 2, 0, 4,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11977 new NutationModel( 4, 1, 2,-2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11978 new NutationModel(-1,-1, 0, 6, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11979 new NutationModel(-3,-1, 2, 6, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11980 new NutationModel(-1, 0, 0, 6, 1, -5.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11981 new NutationModel(-3, 0, 2, 6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11982 new NutationModel( 1,-1, 0, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11983 new NutationModel( 1,-1, 0, 4, 0, 12.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11984
11985 /* 641-650 */
11986 new NutationModel(-2, 0, 2, 5, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11987 new NutationModel( 1,-2, 2, 2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11988 new NutationModel( 3,-1, 0, 2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11989 new NutationModel( 1,-1, 2, 2, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11990 new NutationModel( 0, 0, 2, 3, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11991 new NutationModel(-1, 1, 2, 4, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11992 new NutationModel( 0, 1, 2, 3, 2, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11993 new NutationModel(-1, 0, 4, 2, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11994 new NutationModel( 2, 0, 2, 1, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11995 new NutationModel( 5, 0, 0, 0, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11996
11997 /* 651-660 */
11998 new NutationModel( 2, 1, 2, 1, 2, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11999 new NutationModel( 1, 0, 4, 0, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0),
12000 new NutationModel( 3, 1, 2, 0, 1, 7.0, 0.0, 0.0, -4.0, 0.0, 0.0),
12001 new NutationModel( 3, 0, 4,-2, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
12002 new NutationModel(-2,-1, 2, 6, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0),
12003 new NutationModel( 0, 0, 0, 6, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0),
12004 new NutationModel( 0,-2, 2, 4, 2, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0),
12005 new NutationModel(-2, 0, 2, 6, 1, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0),
12006 new NutationModel( 2, 0, 0, 4, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
12007 new NutationModel( 2, 0, 0, 4, 0, 10.0, 0.0, 0.0, 0.0, 0.0, 0.0),
12008
12009 /* 661-670 */
12010 new NutationModel( 2,-2, 2, 2, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
12011 new NutationModel( 0, 0, 2, 4, 0, 7.0, 0.0, 0.0, 0.0, 0.0, 0.0),
12012 new NutationModel( 1, 0, 2, 3, 2, 7.0, 0.0, 0.0, -3.0, 0.0, 0.0),
12013 new NutationModel( 4, 0, 0, 2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
12014 new NutationModel( 2, 0, 2, 2, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0),
12015 new NutationModel( 0, 0, 4, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
12016 new NutationModel( 4,-1, 2, 0, 2, -6.0, 0.0, 0.0, 2.0, 0.0, 0.0),
12017 new NutationModel( 3, 0, 2, 1, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
12018 new NutationModel( 2, 1, 2, 2, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0),
12019 new NutationModel( 4, 1, 2, 0, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
12020
12021 /* 671-678 */
12022 new NutationModel(-1,-1, 2, 6, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
12023 new NutationModel(-1, 0, 2, 6, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
12024 new NutationModel( 1,-1, 2, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
12025 new NutationModel( 1, 1, 2, 4, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
12026 new NutationModel( 3, 1, 2, 2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
12027 new NutationModel( 5, 0, 2, 0, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
12028 new NutationModel( 2,-1, 2, 4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
12029 new NutationModel( 2, 0, 2, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0)
12030 };
12031
12032 /* Number of terms in the luni-solar nutation model */
12033 final int NLS = xls.length;
12034
12035 /* ------------------------ */
12036 /* Planetary nutation model */
12037 /* ------------------------ */
12038
12039 /* The units for the sine and cosine coefficients are */
12040 /* 0.1 microarcsecond */
12041
12042 final class PlanetaryNutModel {
12043 final int nl, /* coefficients of l, F, D and Omega */
12044 nf,
12045 nd,
12046 nom,
12047 nme, /* coefficients of planetary longitudes */
12048 nve,
12049 nea,
12050 nma,
12051 nju,
12052 nsa,
12053 nur,
12054 nne,
12055 npa; /* coefficient of general precession */
12056 final int sp,cp; /* longitude sin, cos coefficients */
12057 final int se,ce; /* obliquity sin, cos coefficients */
12058 public PlanetaryNutModel( int nl,
12059 int nf,
12060 int nd,
12061 int nom,
12062 int nme,
12063 int nve,
12064 int nea,
12065 int nma,
12066 int nju,
12067 int nsa,
12068 int nur,
12069 int nne,
12070 int npa,
12071 int sp,int cp,
12072 int se,int ce
12073 ) {
12074 this.nl = nl; /* coefficients of l, F, D and Omega */
12075 this.nf = nf;
12076 this.nd = nd;
12077 this.nom = nom;
12078 this.nme = nme; /* coefficients of planetary longitudes */
12079 this.nve = nve;
12080 this.nea = nea;
12081 this.nma = nma;
12082 this.nju = nju;
12083 this.nsa = nsa;
12084 this.nur = nur;
12085 this.nne = nne;
12086 this.npa = npa; /* coefficient of general precession */
12087 this.sp = sp; this.cp = cp; /* longitude sin, cos coefficients */
12088 this.se = se; this.ce = ce; /* obliquity sin, cos coefficients */
12089
12090 }
12091 }
12092
12093 PlanetaryNutModel xpl[] = {
12094
12095 /* 1-10 */
12096 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, 0, 1440, 0, 0, 0),
12097 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -8, 16,-4,-5, 0, 0, 2, 56,-117, -42, -40),
12098 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, 2, 125, -43, 0, -54),
12099 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-1, 2, 2, 0, 5, 0, 0),
12100 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -4, 8,-1,-5, 0, 0, 2, 3, -7, -3, 0),
12101 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 1, 3, 0, 0, -2),
12102 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, 3, -8, 3, 0, 0, 0, 0, -114, 0, 0, 61),
12103 new PlanetaryNutModel(-1, 0, 0, 0, 0, 10, -3, 0, 0, 0, 0, 0, 0, -219, 89, 0, 0),
12104 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0,-2, 6,-3, 0, 2, -3, 0, 0, 0),
12105 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, -462,1604, 0, 0),
12106
12107 /* 11-20 */
12108 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -5, 8,-3, 0, 0, 0, 0, 99, 0, 0, -53),
12109 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -4, 8,-3, 0, 0, 0, 1, -3, 0, 0, 2),
12110 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -8, 1, 5, 0, 0, 2, 0, 6, 2, 0),
12111 new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 6, 4, 0, 0, 0, 0, 2, 3, 0, 0, 0),
12112 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 2,-5, 0, 0, 2, -12, 0, 0, 0),
12113 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 2,-5, 0, 0, 1, 14,-218, 117, 8),
12114 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 2,-5, 0, 0, 0, 31,-481, -257, -17),
12115 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 2,-5, 0, 0, 0, -491, 128, 0, 0),
12116 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0,-2, 5, 0, 0, 0,-3084,5123, 2735,1647),
12117 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0,-2, 5, 0, 0, 1,-1444,2409,-1286,-771),
12118
12119 /* 21-30 */
12120 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0,-2, 5, 0, 0, 2, 11, -24, -11, -9),
12121 new PlanetaryNutModel( 2,-1,-1, 0, 0, 0, 3, -7, 0, 0, 0, 0, 0, 26, -9, 0, 0),
12122 new PlanetaryNutModel( 1, 0,-2, 0, 0, 19,-21, 3, 0, 0, 0, 0, 0, 103, -60, 0, 0),
12123 new PlanetaryNutModel( 0, 1,-1, 1, 0, 2, -4, 0,-3, 0, 0, 0, 0, 0, -13, -7, 0),
12124 new PlanetaryNutModel( 1, 0,-1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0, -26, -29, -16, 14),
12125 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0,-4,10, 0, 0, 0, 9, -27, -14, -5),
12126 new PlanetaryNutModel(-2, 0, 2, 1, 0, 0, 2, 0, 0,-5, 0, 0, 0, 12, 0, 0, -6),
12127 new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -7, 4, 0, 0, 0, 0, 0, -7, 0, 0, 0),
12128 new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 1, 0, 1,-1, 0, 0, 0, 0, 24, 0, 0),
12129 new PlanetaryNutModel(-2, 0, 2, 1, 0, 0, 2, 0,-2, 0, 0, 0, 0, 284, 0, 0,-151),
12130
12131 /* 31-40 */
12132 new PlanetaryNutModel(-1, 0, 0, 0, 0, 18,-16, 0, 0, 0, 0, 0, 0, 226, 101, 0, 0),
12133 new PlanetaryNutModel(-2, 1, 1, 2, 0, 0, 1, 0,-2, 0, 0, 0, 0, 0, -8, -2, 0),
12134 new PlanetaryNutModel(-1, 1,-1, 1, 0, 18,-17, 0, 0, 0, 0, 0, 0, 0, -6, -3, 0),
12135 new PlanetaryNutModel(-1, 0, 1, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 5, 0, 0, -3),
12136 new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 13, 0, 0, 0, 0, 0, 2, -41, 175, 76, 17),
12137 new PlanetaryNutModel( 0, 2,-2, 2, 0, -8, 11, 0, 0, 0, 0, 0, 0, 0, 15, 6, 0),
12138 new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 13, 0, 0, 0, 0, 0, 1, 425, 212, -133, 269),
12139 new PlanetaryNutModel( 0, 1,-1, 1, 0, -8, 12, 0, 0, 0, 0, 0, 0, 1200, 598, 319,-641),
12140 new PlanetaryNutModel( 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, 0, 235, 334, 0, 0),
12141 new PlanetaryNutModel( 0, 1,-1, 1, 0, 8,-14, 0, 0, 0, 0, 0, 0, 11, -12, -7, -6),
12142
12143 /* 41-50 */
12144 new PlanetaryNutModel( 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, 1, 5, -6, 3, 3),
12145 new PlanetaryNutModel(-2, 0, 2, 1, 0, 0, 2, 0,-4, 5, 0, 0, 0, -5, 0, 0, 3),
12146 new PlanetaryNutModel(-2, 0, 2, 2, 0, 3, -3, 0, 0, 0, 0, 0, 0, 6, 0, 0, -3),
12147 new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 2, 0,-3, 1, 0, 0, 0, 15, 0, 0, 0),
12148 new PlanetaryNutModel( 0, 0, 0, 1, 0, 3, -5, 0, 2, 0, 0, 0, 0, 13, 0, 0, -7),
12149 new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 2, 0,-4, 3, 0, 0, 0, -6, -9, 0, 0),
12150 new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 266, -78, 0, 0),
12151 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, -1, 2, 0, 0, 0, 0, 0, -460,-435, -232, 246),
12152 new PlanetaryNutModel( 0, 1,-1, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 15, 7, 0),
12153 new PlanetaryNutModel(-1, 1, 0, 1, 0, 3, -5, 0, 0, 0, 0, 0, 0, -3, 0, 0, 2),
12154
12155 /* 51-60 */
12156 new PlanetaryNutModel(-1, 0, 1, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, 131, 0, 0),
12157 new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 2, 0,-2,-2, 0, 0, 0, 4, 0, 0, 0),
12158 new PlanetaryNutModel(-2, 2, 0, 2, 0, 0, -5, 9, 0, 0, 0, 0, 0, 0, 3, 0, 0),
12159 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 0, 0,-1, 0, 0, 0, 4, 2, 0),
12160 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0),
12161 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 0, 0, 0, 2, 0, -17, -19, -10, 9),
12162 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, -9, -11, 6, -5),
12163 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -6, 0, 0, 3),
12164 new PlanetaryNutModel(-1, 0, 1, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, -16, 8, 0, 0),
12165 new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0),
12166
12167 /* 61-70 */
12168 new PlanetaryNutModel( 0, 1,-1, 2, 0, 0, -1, 0, 0, 2, 0, 0, 0, 11, 24, 11, -5),
12169 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, -9, 17, 0, 0, 0, 0, 0, -3, -4, -2, 1),
12170 new PlanetaryNutModel( 0, 0, 0, 2, 0, -3, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1),
12171 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0,-1, 2, 0, 0, 0, 0, -8, -4, 0),
12172 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 1,-2, 0, 0, 0, 0, 3, 0, 0),
12173 new PlanetaryNutModel( 1, 0,-2, 0, 0, 17,-16, 0,-2, 0, 0, 0, 0, 0, 5, 0, 0),
12174 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 1,-3, 0, 0, 0, 0, 3, 2, 0),
12175 new PlanetaryNutModel(-2, 0, 2, 1, 0, 0, 5, -6, 0, 0, 0, 0, 0, -6, 4, 2, 3),
12176 new PlanetaryNutModel( 0,-2, 2, 0, 0, 0, 9,-13, 0, 0, 0, 0, 0, -3, -5, 0, 0),
12177 new PlanetaryNutModel( 0, 1,-1, 2, 0, 0, -1, 0, 0, 1, 0, 0, 0, -5, 0, 0, 2),
12178
12179 /* 71-80 */
12180 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 24, 13, -2),
12181 new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, -42, 20, 0, 0),
12182 new PlanetaryNutModel( 0,-2, 2, 0, 0, 5, -6, 0, 0, 0, 0, 0, 0, -10, 233, 0, 0),
12183 new PlanetaryNutModel( 0,-1, 1, 1, 0, 5, -7, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1),
12184 new PlanetaryNutModel(-2, 0, 2, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0, 78, -18, 0, 0),
12185 new PlanetaryNutModel( 2, 1,-3, 1, 0, -6, 7, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0),
12186 new PlanetaryNutModel( 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -3, -1, 0),
12187 new PlanetaryNutModel( 0,-1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -4, -2, 1),
12188 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, -8, -4, -1),
12189 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, -5, 3, 0),
12190
12191 /* 81-90 */
12192 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -7, 0, 0, 3),
12193 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 2, -14, 8, 3, 6),
12194 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 1, 0, 8, -4, 0),
12195 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -9, 15, 0, 0, 0, 0, 0, 0, 19, 10, 0),
12196 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0, 45, -22, 0, 0),
12197 new PlanetaryNutModel( 1,-1,-1, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0, -3, 0, 0, 0),
12198 new PlanetaryNutModel( 2, 0,-2, 0, 0, 2, -5, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0),
12199 new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 2, 0,-5, 5, 0, 0, 0, 0, 3, 0, 0),
12200 new PlanetaryNutModel( 2, 0,-2, 1, 0, 0, -6, 8, 0, 0, 0, 0, 0, 3, 5, 3, -2),
12201 new PlanetaryNutModel( 2, 0,-2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0, 89, -16, -9, -48),
12202
12203 /* 91-100 */
12204 new PlanetaryNutModel(-2, 1, 1, 0, 0, 0, 1, 0,-3, 0, 0, 0, 0, 0, 3, 0, 0),
12205 new PlanetaryNutModel(-2, 1, 1, 1, 0, 0, 1, 0,-3, 0, 0, 0, 0, -3, 7, 4, 2),
12206 new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, -349, -62, 0, 0),
12207 new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, -15, 22, 0, 0),
12208 new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 2, 0,-1,-5, 0, 0, 0, -3, 0, 0, 0),
12209 new PlanetaryNutModel(-1, 0, 1, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, -53, 0, 0, 0),
12210 new PlanetaryNutModel(-1, 1, 1, 1, 0,-20, 20, 0, 0, 0, 0, 0, 0, 5, 0, 0, -3),
12211 new PlanetaryNutModel( 1, 0,-2, 0, 0, 20,-21, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0),
12212 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 8,-15, 0, 0, 0, 0, 0, 15, -7, -4, -8),
12213 new PlanetaryNutModel( 0, 2,-2, 1, 0, 0,-10, 15, 0, 0, 0, 0, 0, -3, 0, 0, 1),
12214
12215 /* 101-110 */
12216 new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, -21, -78, 0, 0),
12217 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 20, -70, -37, -11),
12218 new PlanetaryNutModel( 0, 1,-1, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 6, 3, 0),
12219 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0,-2, 4, 0, 0, 0, 5, 3, 2, -2),
12220 new PlanetaryNutModel( 2, 0,-2, 1, 0, -6, 8, 0, 0, 0, 0, 0, 0, -17, -4, -2, 9),
12221 new PlanetaryNutModel( 0,-2, 2, 1, 0, 5, -6, 0, 0, 0, 0, 0, 0, 0, 6, 3, 0),
12222 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0,-1, 0, 0, 1, 32, 15, -8, 17),
12223 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 0,-1, 0, 0, 0, 174, 84, 45, -93),
12224 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 11, 56, 0, 0),
12225 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, -66, -12, -6, 35),
12226
12227 /* 111-120 */
12228 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 47, 8, 4, -25),
12229 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 8, 4, 0),
12230 new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -9, 13, 0, 0, 0, 0, 0, 10, -22, -12, -5),
12231 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 7,-13, 0, 0, 0, 0, 0, -3, 0, 0, 2),
12232 new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, -24, 12, 0, 0),
12233 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 9,-17, 0, 0, 0, 0, 0, 5, -6, 0, 0),
12234 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -9, 17, 0, 0, 0, 0, 2, 3, 0, 0, -2),
12235 new PlanetaryNutModel( 1, 0,-1, 1, 0, 0, -3, 4, 0, 0, 0, 0, 0, 4, 3, 1, -2),
12236 new PlanetaryNutModel( 1, 0,-1, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0, 0, 29, 15, 0),
12237 new PlanetaryNutModel( 0, 0, 0, 2, 0, 0, -1, 2, 0, 0, 0, 0, 0, -5, -4, -2, 2),
12238
12239 /* 121-130 */
12240 new PlanetaryNutModel( 0,-1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, -3, -1, -5),
12241 new PlanetaryNutModel( 0,-2, 2, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0),
12242 new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -5, 0, 2, 0, 0, 0, 0, 10, 0, 0, 0),
12243 new PlanetaryNutModel(-2, 0, 2, 1, 0, 0, 2, 0,-3, 1, 0, 0, 0, 3, 0, 0, -2),
12244 new PlanetaryNutModel(-2, 0, 2, 1, 0, 3, -3, 0, 0, 0, 0, 0, 0, -5, 0, 0, 3),
12245 new PlanetaryNutModel( 0, 0, 0, 1, 0, 8,-13, 0, 0, 0, 0, 0, 0, 46, 66, 35, -25),
12246 new PlanetaryNutModel( 0,-1, 1, 0, 0, 8,-12, 0, 0, 0, 0, 0, 0, -14, 7, 0, 0),
12247 new PlanetaryNutModel( 0, 2,-2, 1, 0, -8, 11, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0),
12248 new PlanetaryNutModel(-1, 0, 1, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -5, 0, 0, 0),
12249 new PlanetaryNutModel(-1, 0, 0, 1, 0, 18,-16, 0, 0, 0, 0, 0, 0, -68, -34, -18, 36),
12250
12251 /* 131-140 */
12252 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0,-1, 1, 0, 0, 0, 0, 14, 7, 0),
12253 new PlanetaryNutModel( 0, 0, 0, 1, 0, 3, -7, 4, 0, 0, 0, 0, 0, 10, -6, -3, -5),
12254 new PlanetaryNutModel(-2, 1, 1, 1, 0, 0, -3, 7, 0, 0, 0, 0, 0, -5, -4, -2, 3),
12255 new PlanetaryNutModel( 0, 1,-1, 2, 0, 0, -1, 0,-2, 5, 0, 0, 0, -3, 5, 2, 1),
12256 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 0, 0,-2, 5, 0, 0, 0, 76, 17, 9, -41),
12257 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, -4, 8,-3, 0, 0, 0, 0, 84, 298, 159, -45),
12258 new PlanetaryNutModel( 1, 0, 0, 1, 0,-10, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1),
12259 new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, -3, 0, 0, 2),
12260 new PlanetaryNutModel(-1, 0, 0, 1, 0, 10, -3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1),
12261 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0, -82, 292, 156, 44),
12262
12263 /* 141-150 */
12264 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 0, 0, 2,-5, 0, 0, 0, -73, 17, 9, 39),
12265 new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 1, 0, 2,-5, 0, 0, 0, -9, -16, 0, 0),
12266 new PlanetaryNutModel( 2,-1,-1, 1, 0, 0, 3, -7, 0, 0, 0, 0, 0, 3, 0, -1, -2),
12267 new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 2, 0, 0,-5, 0, 0, 0, -3, 0, 0, 0),
12268 new PlanetaryNutModel( 0, 0, 0, 1, 0, -3, 7, -4, 0, 0, 0, 0, 0, -9, -5, -3, 5),
12269 new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, -439, 0, 0, 0),
12270 new PlanetaryNutModel( 1, 0, 0, 1, 0,-18, 16, 0, 0, 0, 0, 0, 0, 57, -28, -15, -30),
12271 new PlanetaryNutModel(-2, 1, 1, 1, 0, 0, 1, 0,-2, 0, 0, 0, 0, 0, -6, -3, 0),
12272 new PlanetaryNutModel( 0, 1,-1, 2, 0, -8, 12, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2),
12273 new PlanetaryNutModel( 0, 0, 0, 1, 0, -8, 13, 0, 0, 0, 0, 0, 0, -40, 57, 30, 21),
12274
12275 /* 151-160 */
12276 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 1, 23, 7, 3, -13),
12277 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 273, 80, 43,-146),
12278 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -449, 430, 0, 0),
12279 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0, -8, -47, -25, 4),
12280 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 1, 6, 47, 25, -3),
12281 new PlanetaryNutModel(-1, 0, 1, 1, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, 23, 13, 0),
12282 new PlanetaryNutModel(-1, 0, 1, 1, 0, 0, 3, -4, 0, 0, 0, 0, 0, -3, 0, 0, 2),
12283 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 0,-2, 0, 0, 0, 3, -4, -2, -2),
12284 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 0, 2, 0, 0, 0, -48,-110, -59, 26),
12285 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 51, 114, 61, -27),
12286
12287 /* 161-170 */
12288 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, -133, 0, 0, 57),
12289 new PlanetaryNutModel( 0, 1,-1, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0),
12290 new PlanetaryNutModel( 0, 0, 0, 1, 0, -3, 5, 0, 0, 0, 0, 0, 0, -21, -6, -3, 11),
12291 new PlanetaryNutModel( 0, 1,-1, 2, 0, -3, 4, 0, 0, 0, 0, 0, 0, 0, -3, -1, 0),
12292 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, -2, 4, 0, 0, 0, 0, 0, -11, -21, -11, 6),
12293 new PlanetaryNutModel( 0, 2,-2, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0, -18,-436, -233, 9),
12294 new PlanetaryNutModel( 0,-1, 1, 0, 0, 5, -7, 0, 0, 0, 0, 0, 0, 35, -7, 0, 0),
12295 new PlanetaryNutModel( 0, 0, 0, 1, 0, 5, -8, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0),
12296 new PlanetaryNutModel(-2, 0, 2, 1, 0, 6, -8, 0, 0, 0, 0, 0, 0, 11, -3, -1, -6),
12297 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, -8, 15, 0, 0, 0, 0, 0, -5, -3, -1, 3),
12298
12299 /* 171-180 */
12300 new PlanetaryNutModel(-2, 0, 2, 1, 0, 0, 2, 0,-3, 0, 0, 0, 0, -53, -9, -5, 28),
12301 new PlanetaryNutModel(-2, 0, 2, 1, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0, 3, 2, 1),
12302 new PlanetaryNutModel( 1, 0,-1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 4, 0, 0, -2),
12303 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 3,-5, 0, 0, 0, 0, -4, 0, 0),
12304 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0,-1, 0, 0, 0, 0, -50, 194, 103, 27),
12305 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0,-1, 0, 0, 0, 1, -13, 52, 28, 7),
12306 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -91, 248, 0, 0),
12307 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 6, 49, 26, -3),
12308 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, -6, -47, -25, 3),
12309 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 5, 3, 0),
12310
12311 /* 181-190 */
12312 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 52, 23, 10, -23),
12313 new PlanetaryNutModel( 0, 1,-1, 2, 0, 0, -1, 0, 0,-1, 0, 0, 0, -3, 0, 0, 1),
12314 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 0, 0, 0,-1, 0, 0, 0, 0, 5, 3, 0),
12315 new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 1, 0, 0,-1, 0, 0, 0, -4, 0, 0, 0),
12316 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -7, 13, 0, 0, 0, 0, 2, -4, 8, 3, 2),
12317 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 7,-13, 0, 0, 0, 0, 0, 10, 0, 0, 0),
12318 new PlanetaryNutModel( 2, 0,-2, 1, 0, 0, -5, 6, 0, 0, 0, 0, 0, 3, 0, 0, -2),
12319 new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -8, 11, 0, 0, 0, 0, 0, 0, 8, 4, 0),
12320 new PlanetaryNutModel( 0, 2,-2, 1,-1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 4, 1),
12321 new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0),
12322
12323 /* 191-200 */
12324 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 0, -4, 0, 0, 0),
12325 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 0, 3, 0, 0, 0, -8, 4, 2, 4),
12326 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1, 8, -4, -2, -4),
12327 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 15, 7, 0),
12328 new PlanetaryNutModel(-2, 0, 2, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, -138, 0, 0, 0),
12329 new PlanetaryNutModel( 0, 0, 0, 2, 0, 0, -4, 8,-3, 0, 0, 0, 0, 0, -7, -3, 0),
12330 new PlanetaryNutModel( 0, 0, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -7, -3, 0),
12331 new PlanetaryNutModel( 2, 0,-2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 54, 0, 0, -29),
12332 new PlanetaryNutModel( 0, 1,-1, 2, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 10, 4, 0),
12333 new PlanetaryNutModel( 0, 1,-1, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -7, 0, 0, 3),
12334
12335 /* 201-210 */
12336 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 1, -2, 0, 0, 0, 0, 0, -37, 35, 19, 20),
12337 new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0),
12338 new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 1, 0, 0,-2, 0, 0, 0, -4, 9, 0, 0),
12339 new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -2, 0, 0, 2, 0, 0, 0, 8, 0, 0, -4),
12340 new PlanetaryNutModel( 0, 1,-1, 1, 0, 3, -6, 0, 0, 0, 0, 0, 0, -9, -14, -8, 5),
12341 new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, 1, -3, -9, -5, 3),
12342 new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, 0, -145, 47, 0, 0),
12343 new PlanetaryNutModel( 0, 1,-1, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0, -10, 40, 21, 5),
12344 new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 0, 1, 11, -49, -26, -7),
12345 new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 0, 2,-2150, 0, 0, 932),
12346
12347 /* 211-220 */
12348 new PlanetaryNutModel( 0, 2,-2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0, -12, 0, 0, 5),
12349 new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 0, 2, 85, 0, 0, -37),
12350 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 1, 4, 0, 0, -2),
12351 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, 1, -4, 0, 0, 0, 0, 0, 3, 0, 0, -2),
12352 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, -86, 153, 0, 0),
12353 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 1, -6, 9, 5, 3),
12354 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -3, 4, 0, 0, 0, 0, 0, 9, -13, -7, -5),
12355 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 1, -8, 12, 6, 4),
12356 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 2, -51, 0, 0, 22),
12357 new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 2, -11,-268, -116, 5),
12358
12359 /* 221-230 */
12360 new PlanetaryNutModel( 0, 2,-2, 2, 0, -5, 6, 0, 0, 0, 0, 0, 0, 0, 12, 5, 0),
12361 new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 2, 0, 7, 3, 0),
12362 new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 1, 31, 6, 3, -17),
12363 new PlanetaryNutModel( 0, 1,-1, 1, 0, -5, 7, 0, 0, 0, 0, 0, 0, 140, 27, 14, -75),
12364 new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 1, 57, 11, 6, -30),
12365 new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, 0, -14, -39, 0, 0),
12366 new PlanetaryNutModel( 0, 1,-1, 2, 0, 0, -1, 0,-1, 0, 0, 0, 0, 0, -6, -2, 0),
12367 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 0, 0,-1, 0, 0, 0, 0, 4, 15, 8, -2),
12368 new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 0, 4, 0, 0),
12369 new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -2, 0, 1, 0, 0, 0, 0, -3, 0, 0, 1),
12370
12371 /* 231-240 */
12372 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -6, 11, 0, 0, 0, 0, 2, 0, 11, 5, 0),
12373 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6,-11, 0, 0, 0, 0, 0, 9, 6, 0, 0),
12374 new PlanetaryNutModel( 0, 0, 0, 0,-1, 0, 4, 0, 0, 0, 0, 0, 2, -4, 10, 4, 2),
12375 new PlanetaryNutModel( 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, 0, 5, 3, 0, 0),
12376 new PlanetaryNutModel( 2, 0,-2, 1, 0, -3, 3, 0, 0, 0, 0, 0, 0, 16, 0, 0, -9),
12377 new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 2, 0, 0,-2, 0, 0, 0, -3, 0, 0, 0),
12378 new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -7, 9, 0, 0, 0, 0, 0, 0, 3, 2, -1),
12379 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 4,-5, 0, 0, 2, 7, 0, 0, -3),
12380 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -25, 22, 0, 0),
12381 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 42, 223, 119, -22),
12382
12383 /* 241-250 */
12384 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0, -27,-143, -77, 14),
12385 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 9, 49, 26, -5),
12386 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2,-1166, 0, 0, 505),
12387 new PlanetaryNutModel( 0, 2,-2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, -5, 0, 0, 2),
12388 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 2, -6, 0, 0, 3),
12389 new PlanetaryNutModel( 0, 0, 0, 1, 0, 3, -5, 0, 0, 0, 0, 0, 0, -8, 0, 1, 4),
12390 new PlanetaryNutModel( 0,-1, 1, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0),
12391 new PlanetaryNutModel( 0, 2,-2, 1, 0, -3, 3, 0, 0, 0, 0, 0, 0, 117, 0, 0, -63),
12392 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 2, -4, 0, 0, 0, 0, 0, -4, 8, 4, 2),
12393 new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -4, 4, 0, 0, 0, 0, 0, 3, 0, 0, -2),
12394
12395 /* 251-260 */
12396 new PlanetaryNutModel( 0, 1,-1, 2, 0, -5, 7, 0, 0, 0, 0, 0, 0, -5, 0, 0, 2),
12397 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 31, 0, 0),
12398 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 1, -5, 0, 1, 3),
12399 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -4, 6, 0, 0, 0, 0, 0, 4, 0, 0, -2),
12400 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 1, -4, 0, 0, 2),
12401 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 2, -24, -13, -6, 10),
12402 new PlanetaryNutModel( 0,-1, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0),
12403 new PlanetaryNutModel( 0, 0, 0, 1, 0, 2, -3, 0, 0, 0, 0, 0, 0, 0, -32, -17, 0),
12404 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -5, 9, 0, 0, 0, 0, 2, 8, 12, 5, -3),
12405 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -5, 9, 0, 0, 0, 0, 1, 3, 0, 0, -1),
12406
12407 /* 261-270 */
12408 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, 0, 7, 13, 0, 0),
12409 new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 1, 0,-2, 0, 0, 0, 0, -3, 16, 0, 0),
12410 new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 50, 0, 0, -27),
12411 new PlanetaryNutModel(-2, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -5, -3, 0),
12412 new PlanetaryNutModel( 0,-2, 2, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0),
12413 new PlanetaryNutModel( 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 0, 1, 0, 5, 3, 1),
12414 new PlanetaryNutModel( 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 0, 2, 24, 5, 2, -11),
12415 new PlanetaryNutModel( 0, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 2, 5, -11, -5, -2),
12416 new PlanetaryNutModel( 0, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 1, 30, -3, -2, -16),
12417 new PlanetaryNutModel( 0, 1,-1, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0, 18, 0, 0, -9),
12418
12419 /* 271-280 */
12420 new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 0, 8, 614, 0, 0),
12421 new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 1, 3, -3, -1, -2),
12422 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 6, 17, 9, -3),
12423 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 3, 0, 0, 0, 0, -3, -9, -5, 2),
12424 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 6, 3, -1),
12425 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, -127, 21, 9, 55),
12426 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, 0, 3, 5, 0, 0),
12427 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -4, 8, 0, 0, 0, 0, 2, -6, -10, -4, 3),
12428 new PlanetaryNutModel( 0,-2, 2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 5, 0, 0, 0),
12429 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 2, 16, 9, 4, -7),
12430
12431 /* 281-290 */
12432 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 1, 3, 0, 0, -2),
12433 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, 0, 0, 22, 0, 0),
12434 new PlanetaryNutModel( 0, 0, 0, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 19, 10, 0),
12435 new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0, 7, 0, 0, -4),
12436 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -5, 10, 0, 0, 0, 0, 2, 0, -5, -2, 0),
12437 new PlanetaryNutModel( 0, 0, 0, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0),
12438 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, -9, 3, 1, 4),
12439 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 2, 17, 0, 0, -7),
12440 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 1, 0, -3, -2, -1),
12441 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, -20, 34, 0, 0),
12442
12443 /* 291-300 */
12444 new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 1, -10, 0, 1, 5),
12445 new PlanetaryNutModel( 0, 1,-1, 1, 0, 1, -3, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2),
12446 new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 22, -87, 0, 0),
12447 new PlanetaryNutModel( 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 1, -4, 0, 0, 2),
12448 new PlanetaryNutModel( 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 2, -3, -6, -2, 1),
12449 new PlanetaryNutModel( 0, 0, 0, 0, 0, -7, 11, 0, 0, 0, 0, 0, 2, -16, -3, -1, 7),
12450 new PlanetaryNutModel( 0, 0, 0, 0, 0, -7, 11, 0, 0, 0, 0, 0, 1, 0, -3, -2, 0),
12451 new PlanetaryNutModel( 0,-2, 2, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0),
12452 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, -68, 39, 0, 0),
12453 new PlanetaryNutModel( 0, 2,-2, 1, 0, -4, 4, 0, 0, 0, 0, 0, 0, 27, 0, 0, -14),
12454
12455 /* 301-310 */
12456 new PlanetaryNutModel( 0,-1, 1, 0, 0, 4, -5, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0),
12457 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -25, 0, 0, 0),
12458 new PlanetaryNutModel( 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 0, 1, -12, -3, -2, 6),
12459 new PlanetaryNutModel( 0, 1,-1, 1, 0, -4, 6, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1),
12460 new PlanetaryNutModel( 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 0, 2, 3, 66, 29, -1),
12461 new PlanetaryNutModel( 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 2, 490, 0, 0,-213),
12462 new PlanetaryNutModel( 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 1, -22, 93, 49, 12),
12463 new PlanetaryNutModel( 0, 1,-1, 1, 0, -4, 5, 0, 0, 0, 0, 0, 0, -7, 28, 15, 4),
12464 new PlanetaryNutModel( 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 1, -3, 13, 7, 2),
12465 new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, 0, -46, 14, 0, 0),
12466
12467 /* 311-320 */
12468 new PlanetaryNutModel(-2, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0),
12469 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0),
12470 new PlanetaryNutModel( 0,-1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0),
12471 new PlanetaryNutModel( 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, -28, 0, 0, 15),
12472 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 0, 5, 0, 0, 0, 2, 5, 0, 0, -2),
12473 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, 0, 3, 0, 0),
12474 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 2, -11, 0, 0, 5),
12475 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -7, 12, 0, 0, 0, 0, 2, 0, 3, 1, 0),
12476 new PlanetaryNutModel( 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1),
12477 new PlanetaryNutModel( 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, 25, 106, 57, -13),
12478
12479 /* 321-330 */
12480 new PlanetaryNutModel( 0, 1,-1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 5, 21, 11, -3),
12481 new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 1485, 0, 0, 0),
12482 new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, -7, -32, -17, 4),
12483 new PlanetaryNutModel( 0, 1,-1, 1, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0),
12484 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 2, -6, -3, -2, 3),
12485 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, 2, 30, -6, -2, -13),
12486 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0,-4, 0, 0, 0, 0, -4, 4, 0, 0),
12487 new PlanetaryNutModel( 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0, -19, 0, 0, 10),
12488 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 2, 0, 4, 2, -1),
12489 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 0, 0, 3, 0, 0),
12490
12491 /* 331-340 */
12492 new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -3, 0, 3, 0, 0, 0, 0, 4, 0, 0, -2),
12493 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -3, 7, 0, 0, 0, 0, 2, 0, -3, -1, 0),
12494 new PlanetaryNutModel(-2, 0, 2, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0),
12495 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 2, 5, 3, 1, -2),
12496 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, 0, 11, 0, 0),
12497 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 2, 118, 0, 0, -52),
12498 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 1, 0, -5, -3, 0),
12499 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0,-3, 0, 0, 0, 0, -28, 36, 0, 0),
12500 new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 5, -5, 0, 0),
12501 new PlanetaryNutModel( 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 1, 14, -59, -31, -8),
12502
12503 /* 341-350 */
12504 new PlanetaryNutModel( 0, 1,-1, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 9, 5, 1),
12505 new PlanetaryNutModel( 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 2, -458, 0, 0, 198),
12506 new PlanetaryNutModel( 0, 0, 0, 0, 0, -6, 9, 0, 0, 0, 0, 0, 2, 0, -45, -20, 0),
12507 new PlanetaryNutModel( 0, 0, 0, 0, 0, -6, 9, 0, 0, 0, 0, 0, 1, 9, 0, 0, -5),
12508 new PlanetaryNutModel( 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0),
12509 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 1, 0,-2, 0, 0, 0, 0, 0, -4, -2, -1),
12510 new PlanetaryNutModel( 0, 2,-2, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0, 11, 0, 0, -6),
12511 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 2, 6, 0, 0, -2),
12512 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, -16, 23, 0, 0),
12513 new PlanetaryNutModel( 0, 0, 0, 1, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0),
12514
12515 /* 351-360 */
12516 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 2, -5, 0, 0, 2),
12517 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0,-2, 0, 0, 0, 0, -166, 269, 0, 0),
12518 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 1, 0,-1, 0, 0, 0, 0, 15, 0, 0, -8),
12519 new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 9, 0, 0, 0, 0, 0, 2, 10, 0, 0, -4),
12520 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, -78, 45, 0, 0),
12521 new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0, 2, 0, -5, -2, 0),
12522 new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0, 1, 7, 0, 0, -4),
12523 new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, -5, 328, 0, 0),
12524 new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 1, 3, 0, 0, -2),
12525 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 5, 0, 0, -2),
12526
12527 /* 361-370 */
12528 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 3, 1, 0),
12529 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 0,-3, 0, 0, 0, -3, 0, 0, 0),
12530 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 1,-5, 0, 0, 0, -3, 0, 0, 0),
12531 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, -4, -2, 0),
12532 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0,-1223, -26, 0, 0),
12533 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0,-1, 0, 0, 0, 1, 0, 7, 3, 0),
12534 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0,-3, 5, 0, 0, 0, 3, 0, 0, 0),
12535 new PlanetaryNutModel( 0, 0, 0, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0),
12536 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 0,-2, 0, 0, 0, -6, 20, 0, 0),
12537 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -368, 0, 0, 0),
12538
12539 /* 371-380 */
12540 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 0,-1, 0, 0, 0, -75, 0, 0, 0),
12541 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 11, 0, 0, -6),
12542 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0, 3, 0, 0, -2),
12543 new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 14, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1),
12544 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 2,-5, 0, 0, 0, -13, -30, 0, 0),
12545 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 0, 21, 3, 0, 0),
12546 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 2, -3, 0, 0, 1),
12547 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, -4, 0, 0, 2),
12548 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 8, -27, 0, 0),
12549 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, -8, 3, 0, 0, 0, 0, -19, -11, 0, 0),
12550
12551 /* 381-390 */
12552 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -3, 8,-3, 0, 0, 0, 2, -4, 0, 0, 2),
12553 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0,-2, 5, 0, 0, 2, 0, 5, 2, 0),
12554 new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 12, 0, 0, 0, 0, 0, 2, -6, 0, 0, 2),
12555 new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 12, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0),
12556 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 1,-2, 0, 0, 0, -1, 0, 0, 0),
12557 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, -14, 0, 0, 6),
12558 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0),
12559 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, -74, 0, 0, 32),
12560 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, -3, -1, 0),
12561 new PlanetaryNutModel( 0, 2,-2, 1, 0, -5, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2),
12562
12563 /* 391-400 */
12564 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 8, 11, 0, 0),
12565 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 3, 2, 0),
12566 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, -262, 0, 0, 114),
12567 new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0),
12568 new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, 1, -7, 0, 0, 4),
12569 new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, 2, 0, -27, -12, 0),
12570 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 2, -19, -8, -4, 8),
12571 new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 7, 0, 0, 0, 0, 0, 2, 202, 0, 0, -87),
12572 new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 7, 0, 0, 0, 0, 0, 1, -8, 35, 19, 5),
12573 new PlanetaryNutModel( 0, 1,-1, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0),
12574
12575 /* 401-410 */
12576 new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, 0, 16, -5, 0, 0),
12577 new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 5, 0, 0, -3),
12578 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -3, 0, 0),
12579 new PlanetaryNutModel( 0, 0, 0, 0,-1, 0, 3, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0),
12580 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, -35, -48, -21, 15),
12581 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 6, 0, 0, 0, 0, 2, -3, -5, -2, 1),
12582 new PlanetaryNutModel( 0, 0, 0, 1, 0, 2, -2, 0, 0, 0, 0, 0, 0, 6, 0, 0, -3),
12583 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -6, 9, 0, 0, 0, 0, 2, 3, 0, 0, -1),
12584 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, 0, -5, 0, 0),
12585 new PlanetaryNutModel( 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 1, 12, 55, 29, -6),
12586
12587 /* 411-420 */
12588 new PlanetaryNutModel( 0, 1,-1, 1, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0),
12589 new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -598, 0, 0, 0),
12590 new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 1, -3, -13, -7, 1),
12591 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 2, -5, -7, -3, 2),
12592 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -5, 7, 0, 0, 0, 0, 2, 3, 0, 0, -1),
12593 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, 5, -7, 0, 0),
12594 new PlanetaryNutModel( 0, 0, 0, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2),
12595 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, 16, -6, 0, 0),
12596 new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, 0, 8, -3, 0, 0),
12597 new PlanetaryNutModel( 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 1, 8, -31, -16, -4),
12598
12599 /* 421-430 */
12600 new PlanetaryNutModel( 0, 1,-1, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0),
12601 new PlanetaryNutModel( 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 2, 113, 0, 0, -49),
12602 new PlanetaryNutModel( 0, 0, 0, 0, 0, -7, 10, 0, 0, 0, 0, 0, 2, 0, -24, -10, 0),
12603 new PlanetaryNutModel( 0, 0, 0, 0, 0, -7, 10, 0, 0, 0, 0, 0, 1, 4, 0, 0, -2),
12604 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 27, 0, 0, 0),
12605 new PlanetaryNutModel( 0, 0, 0, 0, 0, -4, 8, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1),
12606 new PlanetaryNutModel( 0, 0, 0, 0, 0, -4, 5, 0, 0, 0, 0, 0, 2, 0, -4, -2, 0),
12607 new PlanetaryNutModel( 0, 0, 0, 0, 0, -4, 5, 0, 0, 0, 0, 0, 1, 5, 0, 0, -2),
12608 new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0),
12609 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, -13, 0, 0, 6),
12610
12611 /* 431-440 */
12612 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 0, 5, 0, 0, 0, 2, 5, 0, 0, -2),
12613 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 2, -18, -10, -4, 8),
12614 new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -4, -28, 0, 0),
12615 new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, -5, 6, 3, 2),
12616 new PlanetaryNutModel( 0, 0, 0, 0, 0, -9, 13, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1),
12617 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 5, 0, 0, 0, 0, 2, -5, -9, -4, 2),
12618 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 2, 17, 0, 0, -7),
12619 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0,-4, 0, 0, 0, 0, 11, 4, 0, 0),
12620 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 7, 0, 0, 0, 0, 2, 0, -6, -2, 0),
12621 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, 83, 15, 0, 0),
12622
12623 /* 441-450 */
12624 new PlanetaryNutModel( 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 0, 1, -4, 0, 0, 2),
12625 new PlanetaryNutModel( 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 0, 2, 0,-114, -49, 0),
12626 new PlanetaryNutModel( 0, 0, 0, 0, 0, -6, 8, 0, 0, 0, 0, 0, 2, 117, 0, 0, -51),
12627 new PlanetaryNutModel( 0, 0, 0, 0, 0, -6, 8, 0, 0, 0, 0, 0, 1, -5, 19, 10, 2),
12628 new PlanetaryNutModel( 0, 0, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0),
12629 new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 2),
12630 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -3, 9, 0, 0, 0, 0, 2, 0, -3, -1, 0),
12631 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 3, 0, 0, 0),
12632 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 2, 0, -6, -2, 0),
12633 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 393, 3, 0, 0),
12634
12635 /* 451-460 */
12636 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 1, -4, 21, 11, 2),
12637 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 2, -6, 0, -1, 3),
12638 new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 10, 0, 0, 0, 0, 0, 2, -3, 8, 4, 1),
12639 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 8, 0, 0, 0),
12640 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 2, 18, -29, -13, -8),
12641 new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 1, 8, 34, 18, -4),
12642 new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0),
12643 new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 1, 3, 12, 6, -1),
12644 new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 2, 54, -15, -7, -24),
12645 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0,-3, 0, 0, 0, 0, 3, 0, 0),
12646
12647 /* 461-470 */
12648 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -5, 13, 0, 0, 0, 0, 2, 3, 0, 0, -1),
12649 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0,-1, 0, 0, 0, 0, 0, 35, 0, 0),
12650 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0,-1, 0, 0, 0, 2, -154, -30, -13, 67),
12651 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0,-2, 0, 0, 0, 15, 0, 0, 0),
12652 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0,-2, 0, 0, 1, 0, 4, 2, 0),
12653 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 9, 0, 0),
12654 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 2, 80, -71, -31, -35),
12655 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0,-1, 0, 0, 2, 0, -20, -9, 0),
12656 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -6, 15, 0, 0, 0, 0, 2, 11, 5, 2, -5),
12657 new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 0, 2, 61, -96, -42, -27),
12658
12659 /* 471-480 */
12660 new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 9, -4, 0, 0, 0, 0, 2, 14, 9, 4, -6),
12661 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 2,-5, 0, 0, 2, -11, -6, -3, 5),
12662 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 8,-1,-5, 0, 0, 2, 0, -3, -1, 0),
12663 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, -8, 3, 0, 0, 0, 2, 123,-415, -180, -53),
12664 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35),
12665 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0),
12666 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 7, -32, -17, -4),
12667 new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -9, -5, 0),
12668 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, -4, 2, 0),
12669 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, -89, 0, 0, 38),
12670
12671 /* 481-490 */
12672 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -6, 16,-4,-5, 0, 0, 2, 0, -86, -19, -6),
12673 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 8,-3, 0, 0, 0, 2, 0, 0, -19, 6),
12674 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 8,-3, 0, 0, 0, 2, -123,-416, -180, 53),
12675 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, -8, 1, 5, 0, 0, 2, 0, -3, -1, 0),
12676 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0,-2, 5, 0, 0, 2, 12, -6, -3, -5),
12677 new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -5, 4, 0, 0, 0, 0, 2, -13, 9, 4, 6),
12678 new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 11, 0, 0, 0, 0, 0, 2, 0, -15, -7, 0),
12679 new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 11, 0, 0, 0, 0, 0, 1, 3, 0, 0, -1),
12680 new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 11, 0, 0, 0, 0, 0, 2, -62, -97, -42, 27),
12681 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 2, -11, 5, 2, 5),
12682
12683 /* 491-500 */
12684 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, -19, -8, 0),
12685 new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -3, 0, 2, 0, 0, 0, 2, -3, 0, 0, 1),
12686 new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, 4, 2, 0),
12687 new PlanetaryNutModel( 0, 1,-1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0),
12688 new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -4, 8,-3, 0, 0, 0, 0, 0, 4, 2, 0),
12689 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, -85, -70, -31, 37),
12690 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 163, -12, -5, -72),
12691 new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 7, 0, 0, 0, 0, 0, 2, -63, -16, -7, 28),
12692 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, -21, -32, -14, 9),
12693 new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 6, 0, 0, 0, 0, 0, 2, 0, -3, -1, 0),
12694
12695 /* 501-510 */
12696 new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 6, 0, 0, 0, 0, 0, 1, 3, 0, 0, -2),
12697 new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0),
12698 new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 2, 3, 10, 4, -1),
12699 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 3, 0, 0, -1),
12700 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 6, 0, 0, 0, 0, 2, 0, -7, -3, 0),
12701 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 7, -9, 0, 0, 0, 0, 2, 0, -4, -2, 0),
12702 new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 6, 19, 0, 0),
12703 new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 2, 5,-173, -75, -2),
12704 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 2, 0, -7, -3, 0),
12705 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 2, 7, -12, -5, -3),
12706
12707 /* 511-520 */
12708 new PlanetaryNutModel( 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, 1, -3, 0, 0, 2),
12709 new PlanetaryNutModel( 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, 2, 3, -4, -2, -1),
12710 new PlanetaryNutModel( 0, 0, 0, 0, 0, -7, 9, 0, 0, 0, 0, 0, 2, 74, 0, 0, -32),
12711 new PlanetaryNutModel( 0, 0, 0, 0, 0, -7, 9, 0, 0, 0, 0, 0, 1, -3, 12, 6, 2),
12712 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 2, 26, -14, -6, -11),
12713 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 2, 19, 0, 0, -8),
12714 new PlanetaryNutModel( 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 1, 6, 24, 13, -3),
12715 new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 83, 0, 0, 0),
12716 new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 1, 0, -10, -5, 0),
12717 new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 2, 11, -3, -1, -5),
12718
12719 /* 521-530 */
12720 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, 3, 0, 1, -1),
12721 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -3, 0, 5, 0, 0, 0, 2, 3, 0, 0, -1),
12722 new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0),
12723 new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 5, -23, -12, -3),
12724 new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, -339, 0, 0, 147),
12725 new PlanetaryNutModel( 0, 0, 0, 0, 0, -9, 12, 0, 0, 0, 0, 0, 2, 0, -10, -5, 0),
12726 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0,-4, 0, 0, 0, 0, 5, 0, 0, 0),
12727 new PlanetaryNutModel( 0, 2,-2, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1),
12728 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 2, 0, -4, -2, 0),
12729 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0,-3, 0, 0, 0, 0, 18, -3, 0, 0),
12730
12731 /* 531-540 */
12732 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0,-3, 0, 0, 0, 2, 9, -11, -5, -4),
12733 new PlanetaryNutModel( 0, 0, 0, 0, 0, -2, 6, 0, 0, 0, 0, 0, 2, -8, 0, 0, 4),
12734 new PlanetaryNutModel( 0, 0, 0, 0, 0, -6, 7, 0, 0, 0, 0, 0, 1, 3, 0, 0, -1),
12735 new PlanetaryNutModel( 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0),
12736 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 2, 6, -9, -4, -2),
12737 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0,-2, 0, 0, 0, 0, -4, -12, 0, 0),
12738 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0,-2, 0, 0, 0, 2, 67, -91, -39, -29),
12739 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 2, 30, -18, -8, -13),
12740 new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
12741 new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 2, 0,-114, -50, 0),
12742
12743 /* 541-550 */
12744 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0,-1, 0, 0, 0, 2, 0, 0, 0, 23),
12745 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0,-1, 0, 0, 0, 2, 517, 16, 7,-224),
12746 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0, 0,-2, 0, 0, 2, 0, -7, -3, 0),
12747 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 2, 143, -3, -1, -62),
12748 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0, 0,-1, 0, 0, 2, 29, 0, 0, -13),
12749 new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, 1, 0,-1, 0, 0, 0, 0, -4, 0, 0, 2),
12750 new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 16, 0, 0, 0, 0, 0, 2, -6, 0, 0, 3),
12751 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0, 2,-5, 0, 0, 2, 5, 12, 5, -2),
12752 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 7, -8, 3, 0, 0, 0, 2, -25, 0, 0, 11),
12753 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -5, 16,-4,-5, 0, 0, 2, -3, 0, 0, 1),
12754
12755 /* 551-560 */
12756 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0),
12757 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 8,-3, 0, 0, 0, 2, -22, 12, 5, 10),
12758 new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 2, 50, 0, 0, -22),
12759 new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 1, 0, 7, 4, 0),
12760 new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 2, 0, 3, 1, 0),
12761 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, -4, 4, 2, 2),
12762 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 2, -5, -11, -5, 2),
12763 new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 8, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0),
12764 new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 5, 0, 0, 0, 0, 0, 1, 4, 17, 9, -2),
12765 new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0),
12766
12767 /* 561-570 */
12768 new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 1, 0, -4, -2, 0),
12769 new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 2, -8, 0, 0, 4),
12770 new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0),
12771 new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 4, -15, -8, -2),
12772 new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 370, -8, 0,-160),
12773 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 2, 0, 0, -3, 0),
12774 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 2, 0, 3, 1, 0),
12775 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, -5, 0, 0, 0, 0, 2, -6, 3, 1, 3),
12776 new PlanetaryNutModel( 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0),
12777 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 2, -10, 0, 0, 4),
12778
12779 /* 571-580 */
12780 new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 0, 2, 0, 9, 4, 0),
12781 new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 4, 17, 7, -2),
12782 new PlanetaryNutModel( 0, 0, 0, 0, 0, -9, 11, 0, 0, 0, 0, 0, 2, 34, 0, 0, -15),
12783 new PlanetaryNutModel( 0, 0, 0, 0, 0, -9, 11, 0, 0, 0, 0, 0, 1, 0, 5, 3, 0),
12784 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, 0,-4, 0, 0, 0, 2, -5, 0, 0, 2),
12785 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, 0,-3, 0, 0, 0, 2, -37, -7, -3, 16),
12786 new PlanetaryNutModel( 0, 0, 0, 0, 0, -6, 6, 0, 0, 0, 0, 0, 1, 3, 13, 7, -2),
12787 new PlanetaryNutModel( 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0),
12788 new PlanetaryNutModel( 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 1, 0, -3, -2, 0),
12789 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, 0,-2, 0, 0, 0, 2, -184, -3, -1, 80),
12790
12791 /* 581-590 */
12792 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 2, -3, 0, 0, 1),
12793 new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0),
12794 new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 1, 0, -10, -6, -1),
12795 new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 2, 31, -6, 0, -13),
12796 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, 0,-1, 0, 0, 0, 2, -3, -32, -14, 1),
12797 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, 0, 0,-2, 0, 0, 2, -7, 0, 0, 3),
12798 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, 0, 0, 2, 0, -8, -4, 0),
12799 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 3, -4, 0, 0),
12800 new PlanetaryNutModel( 0, 0, 0, 0, 0, 8, -9, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0),
12801 new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 0, 2, 0, 3, 1, 0),
12802
12803 /* 591-600 */
12804 new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 19, -23, -10, 2),
12805 new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -10),
12806 new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 3, 2, 0),
12807 new PlanetaryNutModel( 0, 0, 0, 0, 0, -7, 7, 0, 0, 0, 0, 0, 1, 0, 9, 5, -1),
12808 new PlanetaryNutModel( 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0),
12809 new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 1, 0, -7, -4, 0),
12810 new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 2, 8, -4, 0, -4),
12811 new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0),
12812 new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0),
12813 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, 0,-4, 0, 0, 0, 2, -3, 0, 0, 1),
12814
12815 /* 601-610 */
12816 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, 0,-3, 0, 0, 0, 2, -9, 0, 1, 4),
12817 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, 0,-2, 0, 0, 0, 2, 3, 12, 5, -1),
12818 new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 17, -3, -1, 0),
12819 new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 1, 0, 7, 4, 0),
12820 new PlanetaryNutModel( 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0),
12821 new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 1, 0, -5, -3, 0),
12822 new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 2, 14, -3, 0, -1),
12823 new PlanetaryNutModel( 0, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0),
12824 new PlanetaryNutModel( 0, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 1, 0, 0, 0, -5),
12825 new PlanetaryNutModel( 0, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 1, 0, 5, 3, 0),
12826
12827 /* 611-620 */
12828 new PlanetaryNutModel( 0, 0, 0, 0, 0, 9, -9, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0),
12829 new PlanetaryNutModel( 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 0, 1, 0, -3, -2, 0),
12830 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 2, 9, 4, 3),
12831 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4),
12832 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0),
12833 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1, 0, 4, 2, 0),
12834 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 6, 0, 0, -3),
12835 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0),
12836 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1, 0, 3, 1, 0),
12837 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 5, 0, 0, -2),
12838
12839 /* 621-630 */
12840 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, -1),
12841 new PlanetaryNutModel( 1, 0,-2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 0),
12842 new PlanetaryNutModel( 1, 0,-2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0),
12843 new PlanetaryNutModel( 1, 0,-2, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 7, 0, 0, 0),
12844 new PlanetaryNutModel( 1, 0,-2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0),
12845 new PlanetaryNutModel(-1, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0),
12846 new PlanetaryNutModel(-1, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 6, 0, 0, 0),
12847 new PlanetaryNutModel(-1, 0, 2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -4, 0, 0),
12848 new PlanetaryNutModel( 1, 0,-2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -4, 0, 0),
12849 new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 5, 0, 0, 0),
12850
12851 /* 631-640 */
12852 new PlanetaryNutModel(-1, 0, 0, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, -3, 0, 0, 0),
12853 new PlanetaryNutModel(-1, 0, 0, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 4, 0, 0, 0),
12854 new PlanetaryNutModel(-1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0),
12855 new PlanetaryNutModel(-1, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0),
12856 new PlanetaryNutModel( 1,-1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0),
12857 new PlanetaryNutModel(-1, 0, 2, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, 13, 0, 0, 0),
12858 new PlanetaryNutModel(-2, 0, 0, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, 21, 11, 0, 0),
12859 new PlanetaryNutModel( 1, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -5, 0, 0),
12860 new PlanetaryNutModel(-1, 1,-1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -5, -2, 0),
12861 new PlanetaryNutModel( 1, 1,-1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0),
12862
12863 /* 641-650 */
12864 new PlanetaryNutModel(-1, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -5, 0, 0),
12865 new PlanetaryNutModel(-1, 0, 2, 1, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 2),
12866 new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 20, 10, 0, 0),
12867 new PlanetaryNutModel(-1, 0, 2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, -34, 0, 0, 0),
12868 new PlanetaryNutModel(-1, 0, 2, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, -19, 0, 0, 0),
12869 new PlanetaryNutModel( 1, 0,-2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 3, 0, 0, -2),
12870 new PlanetaryNutModel( 1, 2,-2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1),
12871 new PlanetaryNutModel( 1, 2,-2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, -6, 0, 0, 3),
12872 new PlanetaryNutModel( 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0),
12873 new PlanetaryNutModel( 1, 0, 0, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 3, 0, 0, 0),
12874
12875 /* 651-660 */
12876 new PlanetaryNutModel( 0, 0,-2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0),
12877 new PlanetaryNutModel( 0, 0,-2, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 4, 0, 0, 0),
12878 new PlanetaryNutModel( 0, 2, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1),
12879 new PlanetaryNutModel( 0, 2, 0, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 6, 0, 0, -3),
12880 new PlanetaryNutModel( 0, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0, -8, 0, 0, 3),
12881 new PlanetaryNutModel( 0, 2, 0, 2, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0),
12882 new PlanetaryNutModel( 0, 0, 2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 0),
12883 new PlanetaryNutModel( 0, 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -3, -2, 0),
12884 new PlanetaryNutModel( 1, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 126, -63, -27, -55),
12885 new PlanetaryNutModel(-1, 2, 0, 2, 0, 10, -3, 0, 0, 0, 0, 0, 0, -5, 0, 1, 2),
12886
12887 /* 661-670 */
12888 new PlanetaryNutModel( 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -3, 28, 15, 2),
12889 new PlanetaryNutModel( 1, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 5, 0, 1, -2),
12890 new PlanetaryNutModel( 0, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, 9, 4, 1),
12891 new PlanetaryNutModel( 0, 2, 0, 2, 0, 0, -4, 8,-3, 0, 0, 0, 0, 0, 9, 4, -1),
12892 new PlanetaryNutModel(-1, 2, 0, 2, 0, 0, -4, 8,-3, 0, 0, 0, 0, -126, -63, -27, 55),
12893 new PlanetaryNutModel( 2, 2,-2, 2, 0, 0, -2, 0, 3, 0, 0, 0, 0, 3, 0, 0, -1),
12894 new PlanetaryNutModel( 1, 2, 0, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0, 21, -11, -6, -11),
12895 new PlanetaryNutModel( 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0),
12896 new PlanetaryNutModel(-1, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -21, -11, -6, 11),
12897 new PlanetaryNutModel(-2, 2, 2, 2, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 1),
12898
12899 /* 671-680 */
12900 new PlanetaryNutModel( 0, 2, 0, 2, 0, 2, -3, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0),
12901 new PlanetaryNutModel( 0, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0, 8, 0, 0, -4),
12902 new PlanetaryNutModel( 0, 2, 0, 2, 0, 0, 1, 0,-1, 0, 0, 0, 0, -6, 0, 0, 3),
12903 new PlanetaryNutModel( 0, 2, 0, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1),
12904 new PlanetaryNutModel(-1, 2, 2, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 3, 0, 0, -1),
12905 new PlanetaryNutModel( 1, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1),
12906 new PlanetaryNutModel(-1, 2, 2, 2, 0, 0, 2, 0,-3, 0, 0, 0, 0, -5, 0, 0, 2),
12907 new PlanetaryNutModel( 2, 2, 0, 2, 0, 0, 2, 0,-3, 0, 0, 0, 0, 24, -12, -5, -11),
12908 new PlanetaryNutModel( 1, 2, 0, 2, 0, 0, -4, 8,-3, 0, 0, 0, 0, 0, 3, 1, 0),
12909 new PlanetaryNutModel( 1, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, 3, 1, 0),
12910
12911 /* 681-687 */
12912 new PlanetaryNutModel( 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0),
12913 new PlanetaryNutModel( 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, -24, -12, -5, 10),
12914 new PlanetaryNutModel( 2, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 4, 0, -1, -2),
12915 new PlanetaryNutModel(-1, 2, 2, 2, 0, 0, 2, 0,-2, 0, 0, 0, 0, 13, 0, 0, -6),
12916 new PlanetaryNutModel(-1, 2, 2, 2, 0, 3, -3, 0, 0, 0, 0, 0, 0, 7, 0, 0, -3),
12917 new PlanetaryNutModel( 1, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1),
12918 new PlanetaryNutModel( 0, 2, 2, 2, 0, 0, 2, 0,-2, 0, 0, 0, 0, 3, 0, 0, -1)
12919 };
12920
12921 /* Number of terms in the planetary nutation model */
12922 final int NPL = xpl.length;
12923
12924 /*--------------------------------------------------------------------*/
12925
12926 /* Interval between fundamental date J2000.0 and given date (JC). */
12927 t = ((date1 - DJ00) + date2) / DJC;
12928
12929 /* ------------------- */
12930 /* LUNI-SOLAR NUTATION */
12931 /* ------------------- */
12932
12933 /* Fundamental (Delaunay) arguments */
12934
12935 /* Mean anomaly of the Moon (IERS 2003). */
12936 el = jauFal03(t);
12937
12938 /* Mean anomaly of the Sun (MHB2000). */
12939 elp = fmod(1287104.79305 +
12940 t * (129596581.0481 +
12941 t * (-0.5532 +
12942 t * (0.000136 +
12943 t * (-0.00001149)))), TURNAS) * DAS2R;
12944
12945 /* Mean longitude of the Moon minus that of the ascending node */
12946 /* (IERS 2003. */
12947 f = jauFaf03(t);
12948
12949 /* Mean elongation of the Moon from the Sun (MHB2000). */
12950 d = fmod(1072260.70369 +
12951 t * (1602961601.2090 +
12952 t * (-6.3706 +
12953 t * (0.006593 +
12954 t * (-0.00003169)))), TURNAS) * DAS2R;
12955
12956 /* Mean longitude of the ascending node of the Moon (IERS 2003). */
12957 om = jauFaom03(t);
12958
12959 /* Initialize the nutation values. */
12960 dp = 0.0;
12961 de = 0.0;
12962
12963 /* Summation of luni-solar nutation series (in reverse order). */
12964 for (i = NLS-1; i >= 0; i--) {
12965
12966 /* Argument and functions. */
12967 arg = fmod((double)xls[i].nl * el +
12968 (double)xls[i].nlp * elp +
12969 (double)xls[i].nf * f +
12970 (double)xls[i].nd * d +
12971 (double)xls[i].nom * om, D2PI);
12972 sarg = sin(arg);
12973 carg = cos(arg);
12974
12975 /* Term. */
12976 dp += (xls[i].sp + xls[i].spt * t) * sarg + xls[i].cp * carg;
12977 de += (xls[i].ce + xls[i].cet * t) * carg + xls[i].se * sarg;
12978 }
12979
12980 /* Convert from 0.1 microarcsec units to radians. */
12981 dpsils = dp * U2R;
12982 depsls = de * U2R;
12983
12984 /* ------------------ */
12985 /* PLANETARY NUTATION */
12986 /* ------------------ */
12987
12988 /* n.b. The MHB2000 code computes the luni-solar and planetary nutation */
12989 /* in different functions, using slightly different Delaunay */
12990 /* arguments in the two cases. This behaviour is faithfully */
12991 /* reproduced here. Use of the IERS 2003 expressions for both */
12992 /* cases leads to negligible changes, well below */
12993 /* 0.1 microarcsecond. */
12994
12995 /* Mean anomaly of the Moon (MHB2000). */
12996 al = fmod(2.35555598 + 8328.6914269554 * t, D2PI);
12997
12998 /* Mean longitude of the Moon minus that of the ascending node */
12999 /*(MHB2000). */
13000 af = fmod(1.627905234 + 8433.466158131 * t, D2PI);
13001
13002 /* Mean elongation of the Moon from the Sun (MHB2000). */
13003 ad = fmod(5.198466741 + 7771.3771468121 * t, D2PI);
13004
13005 /* Mean longitude of the ascending node of the Moon (MHB2000). */
13006 aom = fmod(2.18243920 - 33.757045 * t, D2PI);
13007
13008 /* General accumulated precession in longitude (IERS 2003). */
13009 apa = jauFapa03(t);
13010
13011 /* Planetary longitudes, Mercury through Uranus (IERS 2003). */
13012 alme = jauFame03(t);
13013 alve = jauFave03(t);
13014 alea = jauFae03(t);
13015 alma = jauFama03(t);
13016 alju = jauFaju03(t);
13017 alsa = jauFasa03(t);
13018 alur = jauFaur03(t);
13019
13020 /* Neptune longitude (MHB2000). */
13021 alne = fmod(5.321159000 + 3.8127774000 * t, D2PI);
13022
13023 /* Initialize the nutation values. */
13024 dp = 0.0;
13025 de = 0.0;
13026
13027 /* Summation of planetary nutation series (in reverse order). */
13028 for (i = NPL-1; i >= 0; i--) {
13029
13030 /* Argument and functions. */
13031 arg = fmod((double)xpl[i].nl * al +
13032 (double)xpl[i].nf * af +
13033 (double)xpl[i].nd * ad +
13034 (double)xpl[i].nom * aom +
13035 (double)xpl[i].nme * alme +
13036 (double)xpl[i].nve * alve +
13037 (double)xpl[i].nea * alea +
13038 (double)xpl[i].nma * alma +
13039 (double)xpl[i].nju * alju +
13040 (double)xpl[i].nsa * alsa +
13041 (double)xpl[i].nur * alur +
13042 (double)xpl[i].nne * alne +
13043 (double)xpl[i].npa * apa, D2PI);
13044 sarg = sin(arg);
13045 carg = cos(arg);
13046
13047 /* Term. */
13048 dp += (double)xpl[i].sp * sarg + (double)xpl[i].cp * carg;
13049 de += (double)xpl[i].se * sarg + (double)xpl[i].ce * carg;
13050
13051 }
13052
13053 /* Convert from 0.1 microarcsec units to radians. */
13054 dpsipl = dp * U2R;
13055 depspl = de * U2R;
13056
13057 /* ------- */
13058 /* RESULTS */
13059 /* ------- */
13060
13061 /* Add luni-solar and planetary components. */
13062 return new NutationTerms( dpsils + dpsipl,
13063 depsls + depspl);
13064 }
13065
13066
13067 /**
13068 * Nutation, IAU 2000B model.
13069 *
13070 *<p>This function is derived from the International Astronomical Union's
13071 * SOFA (Standards Of Fundamental Astronomy) software collection.
13072 *
13073 *<p>Status: canonical model.
13074 *
13075 *<!-- Given: -->
13076 * @param date1 double TT as a 2-part Julian Date (Note 1)
13077 * @param date2 double TT as a 2-part Julian Date (Note 1)
13078 *
13079 *<!-- Returned: -->
13080 * @return nutation, luni-solar + planetary (Note 2)
13081 *
13082 * <p>Notes:
13083 * <ol>
13084 *
13085 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
13086 * convenient way between the two arguments. For example,
13087 * JD(TT)=2450123.7 could be expressed in any of these ways,
13088 * among others:
13089 *<pre>
13090 * date1 date2
13091 *
13092 * 2450123.7 0.0 (JD method)
13093 * 2451545.0 -1421.3 (J2000 method)
13094 * 2400000.5 50123.2 (MJD method)
13095 * 2450123.5 0.2 (date & time method)
13096 *</pre>
13097 * The JD method is the most natural and convenient to use in
13098 * cases where the loss of several decimal digits of resolution
13099 * is acceptable. The J2000 method is best matched to the way
13100 * the argument is handled internally and will deliver the
13101 * optimum resolution. The MJD method and the date & time methods
13102 * are both good compromises between resolution and convenience.
13103 *
13104 * <li> The nutation components in longitude and obliquity are in radians
13105 * and with respect to the equinox and ecliptic of date. The
13106 * obliquity at J2000.0 is assumed to be the Lieske et al. (1977)
13107 * value of 84381.448 arcsec. (The errors that result from using
13108 * this function with the IAU 2006 value of 84381.406 arcsec can be
13109 * neglected.)
13110 *
13111 * The nutation model consists only of luni-solar terms, but
13112 * includes also a fixed offset which compensates for certain long-
13113 * period planetary terms (Note 7).
13114 *
13115 * <li> This function is an implementation of the IAU 2000B abridged
13116 * nutation model formally adopted by the IAU General Assembly in
13117 * 2000. The function computes the MHB_2000_SHORT luni-solar
13118 * nutation series (Luzum 2001), but without the associated
13119 * corrections for the precession rate adjustments and the offset
13120 * between the GCRS and J2000.0 mean poles.
13121 *
13122 * <li> The full IAU 2000A (MHB2000) nutation model contains nearly 1400
13123 * terms. The IAU 2000B model (McCarthy & Luzum 2003) contains only
13124 * 77 terms, plus additional simplifications, yet still delivers
13125 * results of 1 mas accuracy at present epochs. This combination of
13126 * accuracy and size makes the IAU 2000B abridged nutation model
13127 * suitable for most practical applications.
13128 *
13129 * The function delivers a pole accurate to 1 mas from 1900 to 2100
13130 * (usually better than 1 mas, very occasionally just outside
13131 * 1 mas). The full IAU 2000A model, which is implemented in the
13132 * function jauNut00a (q.v.), delivers considerably greater accuracy
13133 * at current dates; however, to realize this improved accuracy,
13134 * corrections for the essentially unpredictable free-core-nutation
13135 * (FCN) must also be included.
13136 *
13137 * <li> The present function provides classical nutation. The
13138 * MHB_2000_SHORT algorithm, from which it is adapted, deals also
13139 * with (i) the offsets between the GCRS and mean poles and (ii) the
13140 * adjustments in longitude and obliquity due to the changed
13141 * precession rates. These additional functions, namely frame bias
13142 * and precession adjustments, are supported by the JSOFA functions
13143 * jauBi00 and jauPr00.
13144 *
13145 * <li> The MHB_2000_SHORT algorithm also provides "total" nutations,
13146 * comprising the arithmetic sum of the frame bias, precession
13147 * adjustments, and nutation (luni-solar + planetary). These total
13148 * nutations can be used in combination with an existing IAU 1976
13149 * precession implementation, such as jauPmat76, to deliver GCRS-
13150 * to-true predictions of mas accuracy at current epochs. However,
13151 * for symmetry with the jauNut00a function (q.v. for the reasons),
13152 * the JSOFA functions do not generate the "total nutations"
13153 * directly. Should they be required, they could of course easily
13154 * be generated by calling jauBi00, jauPr00 and the present function
13155 * and adding the results.
13156 *
13157 * <li> The IAU 2000B model includes "planetary bias" terms that are
13158 * fixed in size but compensate for long-period nutations. The
13159 * amplitudes quoted in McCarthy & Luzum (2003), namely
13160 * Dpsi = -1.5835 mas and Depsilon = +1.6339 mas, are optimized for
13161 * the "total nutations" method described in Note 6. The Luzum
13162 * (2001) values used in this JSOFA implementation, namely -0.135 mas
13163 * and +0.388 mas, are optimized for the "rigorous" method, where
13164 * frame bias, precession and nutation are applied separately and in
13165 * that order. During the interval 1995-2050, the JSOFA
13166 * implementation delivers a maximum error of 1.001 mas (not
13167 * including FCN).
13168 *</ol>
13169 *<p>References:
13170 *
13171 * <p>Lieske, J.H., Lederle, T., Fricke, W., Morando, B., "Expressions
13172 * for the precession quantities based upon the IAU /1976/ system of
13173 * astronomical constants", Astron.Astrophys. 58, 1-2, 1-16. (1977)
13174 *
13175 * <p>Luzum, B., private communication, 2001 (Fortran code
13176 * MHB_2000_SHORT)
13177 *
13178 * <p>McCarthy, D.D. & Luzum, B.J., "An abridged model of the
13179 * precession-nutation of the celestial pole", Cel.Mech.Dyn.Astron.
13180 * 85, 37-49 (2003)
13181 *
13182 * <p>Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
13183 * Francou, G., Laskar, J., Astron.Astrophys. 282, 663-683 (1994)
13184 *
13185 *@version 2009 December 17
13186 *
13187 * @since Release 20101201
13188 *
13189 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
13190 */
13191 public static NutationTerms jauNut00b(double date1, double date2)
13192 {
13193 double t, el, elp, f, d, om, arg, dp, de, sarg, carg,
13194 dpsils, depsls, dpsipl, depspl;
13195 int i;
13196
13197 /* Units of 0.1 microarcsecond to radians */
13198 final double U2R = DAS2R / 1e7;
13199
13200 /* ---------------------------------------- */
13201 /* Fixed offsets in lieu of planetary terms */
13202 /* ---------------------------------------- */
13203
13204 final double DPPLAN = -0.135 * DMAS2R;
13205 final double DEPLAN = 0.388 * DMAS2R;
13206
13207 /* --------------------------------------------------- */
13208 /* Luni-solar nutation: argument and term coefficients */
13209 /* --------------------------------------------------- */
13210
13211 /* The units for the sine and cosine coefficients are */
13212 /* 0.1 microarcsec and the same per Julian century */
13213
13214 final class LSNutationModel
13215 {
13216 final int nl,nlp,nf,nd,nom; /* coefficients of l,l',F,D,Om */
13217 final double ps,pst,pc; /* longitude sin, t*sin, cos coefficients */
13218 final double ec,ect,es; /* obliquity cos, t*cos, sin coefficients */
13219
13220 public LSNutationModel( int nl,int nlp,int nf,int nd,int nom,
13221 double ps, double pst, double pc,
13222 double ec, double ect, double es ) {
13223 this.nl = nl;this.nlp = nlp;this.nf = nf;this.nd = nd;this.nom = nom;
13224 this.ps = ps;this.pst = pst;this.pc = pc;
13225 this.ec = ec;this.ect = ect; this.es= es;
13226 }
13227
13228 }
13229 LSNutationModel x[] = {
13230
13231 /* 1-10 */
13232 new LSNutationModel( 0, 0, 0, 0,1,
13233 -172064161.0, -174666.0, 33386.0, 92052331.0, 9086.0, 15377.0),
13234 new LSNutationModel( 0, 0, 2,-2,2,
13235 -13170906.0, -1675.0, -13696.0, 5730336.0, -3015.0, -4587.0),
13236 new LSNutationModel( 0, 0, 2, 0,2,-2276413.0,-234.0, 2796.0, 978459.0,-485.0,1374.0),
13237 new LSNutationModel( 0, 0, 0, 0,2,2074554.0, 207.0, -698.0,-897492.0, 470.0,-291.0),
13238 new LSNutationModel( 0, 1, 0, 0,0,1475877.0,-3633.0,11817.0, 73871.0,-184.0,-1924.0),
13239 new LSNutationModel( 0, 1, 2,-2,2,-516821.0, 1226.0, -524.0, 224386.0,-677.0,-174.0),
13240 new LSNutationModel( 1, 0, 0, 0,0, 711159.0, 73.0, -872.0, -6750.0, 0.0, 358.0),
13241 new LSNutationModel( 0, 0, 2, 0,1,-387298.0, -367.0, 380.0, 200728.0, 18.0, 318.0),
13242 new LSNutationModel( 1, 0, 2, 0,2,-301461.0, -36.0, 816.0, 129025.0, -63.0, 367.0),
13243 new LSNutationModel( 0,-1, 2,-2,2, 215829.0, -494.0, 111.0, -95929.0, 299.0, 132.0),
13244
13245 /* 11-20 */
13246 new LSNutationModel( 0, 0, 2,-2,1, 128227.0, 137.0, 181.0, -68982.0, -9.0, 39.0),
13247 new LSNutationModel(-1, 0, 2, 0,2, 123457.0, 11.0, 19.0, -53311.0, 32.0, -4.0),
13248 new LSNutationModel(-1, 0, 0, 2,0, 156994.0, 10.0, -168.0, -1235.0, 0.0, 82.0),
13249 new LSNutationModel( 1, 0, 0, 0,1, 63110.0, 63.0, 27.0, -33228.0, 0.0, -9.0),
13250 new LSNutationModel(-1, 0, 0, 0,1, -57976.0, -63.0, -189.0, 31429.0, 0.0, -75.0),
13251 new LSNutationModel(-1, 0, 2, 2,2, -59641.0, -11.0, 149.0, 25543.0, -11.0, 66.0),
13252 new LSNutationModel( 1, 0, 2, 0,1, -51613.0, -42.0, 129.0, 26366.0, 0.0, 78.0),
13253 new LSNutationModel(-2, 0, 2, 0,1, 45893.0, 50.0, 31.0, -24236.0, -10.0, 20.0),
13254 new LSNutationModel( 0, 0, 0, 2,0, 63384.0, 11.0, -150.0, -1220.0, 0.0, 29.0),
13255 new LSNutationModel( 0, 0, 2, 2,2, -38571.0, -1.0, 158.0, 16452.0, -11.0, 68.0),
13256
13257 /* 21-30 */
13258 new LSNutationModel( 0,-2, 2,-2,2, 32481.0, 0.0, 0.0, -13870.0, 0.0, 0.0),
13259 new LSNutationModel(-2, 0, 0, 2,0, -47722.0, 0.0, -18.0, 477.0, 0.0, -25.0),
13260 new LSNutationModel( 2, 0, 2, 0,2, -31046.0, -1.0, 131.0, 13238.0, -11.0, 59.0),
13261 new LSNutationModel( 1, 0, 2,-2,2, 28593.0, 0.0, -1.0, -12338.0, 10.0, -3.0),
13262 new LSNutationModel(-1, 0, 2, 0,1, 20441.0, 21.0, 10.0, -10758.0, 0.0, -3.0),
13263 new LSNutationModel( 2, 0, 0, 0,0, 29243.0, 0.0, -74.0, -609.0, 0.0, 13.0),
13264 new LSNutationModel( 0, 0, 2, 0,0, 25887.0, 0.0, -66.0, -550.0, 0.0, 11.0),
13265 new LSNutationModel( 0, 1, 0, 0,1, -14053.0, -25.0, 79.0, 8551.0, -2.0, -45.0),
13266 new LSNutationModel(-1, 0, 0, 2,1, 15164.0, 10.0, 11.0, -8001.0, 0.0, -1.0),
13267 new LSNutationModel( 0, 2, 2,-2,2, -15794.0, 72.0, -16.0, 6850.0, -42.0, -5.0),
13268
13269 /* 31-40 */
13270 new LSNutationModel( 0, 0,-2, 2,0, 21783.0, 0.0, 13.0, -167.0, 0.0, 13.0),
13271 new LSNutationModel( 1, 0, 0,-2,1, -12873.0, -10.0, -37.0, 6953.0, 0.0, -14.0),
13272 new LSNutationModel( 0,-1, 0, 0,1, -12654.0, 11.0, 63.0, 6415.0, 0.0, 26.0),
13273 new LSNutationModel(-1, 0, 2, 2,1, -10204.0, 0.0, 25.0, 5222.0, 0.0, 15.0),
13274 new LSNutationModel( 0, 2, 0, 0,0, 16707.0, -85.0, -10.0, 168.0, -1.0, 10.0),
13275 new LSNutationModel( 1, 0, 2, 2,2, -7691.0, 0.0, 44.0, 3268.0, 0.0, 19.0),
13276 new LSNutationModel(-2, 0, 2, 0,0, -11024.0, 0.0, -14.0, 104.0, 0.0, 2.0),
13277 new LSNutationModel( 0, 1, 2, 0,2, 7566.0, -21.0, -11.0, -3250.0, 0.0, -5.0),
13278 new LSNutationModel( 0, 0, 2, 2,1, -6637.0, -11.0, 25.0, 3353.0, 0.0, 14.0),
13279 new LSNutationModel( 0,-1, 2, 0,2, -7141.0, 21.0, 8.0, 3070.0, 0.0, 4.0),
13280
13281 /* 41-50 */
13282 new LSNutationModel( 0, 0, 0, 2,1, -6302.0, -11.0, 2.0, 3272.0, 0.0, 4.0),
13283 new LSNutationModel( 1, 0, 2,-2,1, 5800.0, 10.0, 2.0, -3045.0, 0.0, -1.0),
13284 new LSNutationModel( 2, 0, 2,-2,2, 6443.0, 0.0, -7.0, -2768.0, 0.0, -4.0),
13285 new LSNutationModel(-2, 0, 0, 2,1, -5774.0, -11.0, -15.0, 3041.0, 0.0, -5.0),
13286 new LSNutationModel( 2, 0, 2, 0,1, -5350.0, 0.0, 21.0, 2695.0, 0.0, 12.0),
13287 new LSNutationModel( 0,-1, 2,-2,1, -4752.0, -11.0, -3.0, 2719.0, 0.0, -3.0),
13288 new LSNutationModel( 0, 0, 0,-2,1, -4940.0, -11.0, -21.0, 2720.0, 0.0, -9.0),
13289 new LSNutationModel(-1,-1, 0, 2,0, 7350.0, 0.0, -8.0, -51.0, 0.0, 4.0),
13290 new LSNutationModel( 2, 0, 0,-2,1, 4065.0, 0.0, 6.0, -2206.0, 0.0, 1.0),
13291 new LSNutationModel( 1, 0, 0, 2,0, 6579.0, 0.0, -24.0, -199.0, 0.0, 2.0),
13292
13293 /* 51-60 */
13294 new LSNutationModel( 0, 1, 2,-2,1, 3579.0, 0.0, 5.0, -1900.0, 0.0, 1.0),
13295 new LSNutationModel( 1,-1, 0, 0,0, 4725.0, 0.0, -6.0, -41.0, 0.0, 3.0),
13296 new LSNutationModel(-2, 0, 2, 0,2, -3075.0, 0.0, -2.0, 1313.0, 0.0, -1.0),
13297 new LSNutationModel( 3, 0, 2, 0,2, -2904.0, 0.0, 15.0, 1233.0, 0.0, 7.0),
13298 new LSNutationModel( 0,-1, 0, 2,0, 4348.0, 0.0, -10.0, -81.0, 0.0, 2.0),
13299 new LSNutationModel( 1,-1, 2, 0,2, -2878.0, 0.0, 8.0, 1232.0, 0.0, 4.0),
13300 new LSNutationModel( 0, 0, 0, 1,0, -4230.0, 0.0, 5.0, -20.0, 0.0, -2.0),
13301 new LSNutationModel(-1,-1, 2, 2,2, -2819.0, 0.0, 7.0, 1207.0, 0.0, 3.0),
13302 new LSNutationModel(-1, 0, 2, 0,0, -4056.0, 0.0, 5.0, 40.0, 0.0, -2.0),
13303 new LSNutationModel( 0,-1, 2, 2,2, -2647.0, 0.0, 11.0, 1129.0, 0.0, 5.0),
13304
13305 /* 61-70 */
13306 new LSNutationModel(-2, 0, 0, 0,1, -2294.0, 0.0, -10.0, 1266.0, 0.0, -4.0),
13307 new LSNutationModel( 1, 1, 2, 0,2, 2481.0, 0.0, -7.0, -1062.0, 0.0, -3.0),
13308 new LSNutationModel( 2, 0, 0, 0,1, 2179.0, 0.0, -2.0, -1129.0, 0.0, -2.0),
13309 new LSNutationModel(-1, 1, 0, 1,0, 3276.0, 0.0, 1.0, -9.0, 0.0, 0.0),
13310 new LSNutationModel( 1, 1, 0, 0,0, -3389.0, 0.0, 5.0, 35.0, 0.0, -2.0),
13311 new LSNutationModel( 1, 0, 2, 0,0, 3339.0, 0.0, -13.0, -107.0, 0.0, 1.0),
13312 new LSNutationModel(-1, 0, 2,-2,1, -1987.0, 0.0, -6.0, 1073.0, 0.0, -2.0),
13313 new LSNutationModel( 1, 0, 0, 0,2, -1981.0, 0.0, 0.0, 854.0, 0.0, 0.0),
13314 new LSNutationModel(-1, 0, 0, 1,0, 4026.0, 0.0, -353.0, -553.0, 0.0,-139.0),
13315 new LSNutationModel( 0, 0, 2, 1,2, 1660.0, 0.0, -5.0, -710.0, 0.0, -2.0),
13316
13317 /* 71-77 */
13318 new LSNutationModel(-1, 0, 2, 4,2, -1521.0, 0.0, 9.0, 647.0, 0.0, 4.0),
13319 new LSNutationModel(-1, 1, 0, 1,1, 1314.0, 0.0, 0.0, -700.0, 0.0, 0.0),
13320 new LSNutationModel( 0,-2, 2,-2,1, -1283.0, 0.0, 0.0, 672.0, 0.0, 0.0),
13321 new LSNutationModel( 1, 0, 2, 2,1, -1331.0, 0.0, 8.0, 663.0, 0.0, 4.0),
13322 new LSNutationModel(-2, 0, 2, 2,2, 1383.0, 0.0, -2.0, -594.0, 0.0, -2.0),
13323 new LSNutationModel(-1, 0, 0, 0,2, 1405.0, 0.0, 4.0, -610.0, 0.0, 2.0),
13324 new LSNutationModel( 1, 1, 2,-2,2, 1290.0, 0.0, 0.0, -556.0, 0.0, 0.0)
13325 };
13326
13327 /* Number of terms in the series */
13328 final int NLS = x.length;
13329
13330 /*--------------------------------------------------------------------*/
13331
13332 /* Interval between fundamental epoch J2000.0 and given date (JC). */
13333 t = ((date1 - DJ00) + date2) / DJC;
13334
13335 /* --------------------*/
13336 /* LUNI-SOLAR NUTATION */
13337 /* --------------------*/
13338
13339 /* Fundamental (Delaunay) arguments from Simon et al. (1994) */
13340
13341 /* Mean anomaly of the Moon. */
13342 el = fmod(485868.249036 + (1717915923.2178) * t, TURNAS) * DAS2R;
13343
13344 /* Mean anomaly of the Sun. */
13345 elp = fmod(1287104.79305 + (129596581.0481) * t, TURNAS) * DAS2R;
13346
13347 /* Mean argument of the latitude of the Moon. */
13348 f = fmod(335779.526232 + (1739527262.8478) * t, TURNAS) * DAS2R;
13349
13350 /* Mean elongation of the Moon from the Sun. */
13351 d = fmod(1072260.70369 + (1602961601.2090) * t, TURNAS) * DAS2R;
13352
13353 /* Mean longitude of the ascending node of the Moon. */
13354 om = fmod(450160.398036 + (-6962890.5431) * t, TURNAS) * DAS2R;
13355
13356 /* Initialize the nutation values. */
13357 dp = 0.0;
13358 de = 0.0;
13359
13360 /* Summation of luni-solar nutation series (smallest terms first). */
13361 for (i = NLS-1; i >= 0; i--) {
13362
13363 /* Argument and functions. */
13364 arg = fmod( (double)x[i].nl * el +
13365 (double)x[i].nlp * elp +
13366 (double)x[i].nf * f +
13367 (double)x[i].nd * d +
13368 (double)x[i].nom * om, D2PI );
13369 sarg = sin(arg);
13370 carg = cos(arg);
13371
13372 /* Term. */
13373 dp += (x[i].ps + x[i].pst * t) * sarg + x[i].pc * carg;
13374 de += (x[i].ec + x[i].ect * t) * carg + x[i].es * sarg;
13375 }
13376
13377 /* Convert from 0.1 microarcsec units to radians. */
13378 dpsils = dp * U2R;
13379 depsls = de * U2R;
13380
13381 /* ------------------------------*/
13382 /* IN LIEU OF PLANETARY NUTATION */
13383 /* ------------------------------*/
13384
13385 /* Fixed offset to correct for missing terms in truncated series. */
13386 dpsipl = DPPLAN;
13387 depspl = DEPLAN;
13388
13389 /* --------*/
13390 /* RESULTS */
13391 /* --------*/
13392
13393 /* Add luni-solar and planetary components. */
13394 return new NutationTerms( dpsils + dpsipl,
13395 depsls + depspl);
13396
13397 }
13398
13399
13400 /**
13401 * IAU 2000A nutation with adjustments to match the IAU 2006
13402 * precession.
13403 *
13404 *<!-- Given: -->
13405 * @param date1 double TT as a 2-part Julian Date (Note 1)
13406 * @param date2 double TT as a 2-part Julian Date (Note 1)
13407 *
13408 *<!-- Returned: -->
13409 * @return nutation, luni-solar + planetary (Note 2)
13410 *
13411 *<p>Status: canonical model.
13412 *
13413 * <p>Notes:
13414 * <ol>
13415 *
13416 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
13417 * convenient way between the two arguments. For example,
13418 * JD(TT)=2450123.7 could be expressed in any of these ways,
13419 * among others:
13420 *<pre>
13421 * date1 date2
13422 *
13423 * 2450123.7 0.0 (JD method)
13424 * 2451545.0 -1421.3 (J2000 method)
13425 * 2400000.5 50123.2 (MJD method)
13426 * 2450123.5 0.2 (date & time method)
13427 *</pre>
13428 * The JD method is the most natural and convenient to use in
13429 * cases where the loss of several decimal digits of resolution
13430 * is acceptable. The J2000 method is best matched to the way
13431 * the argument is handled internally and will deliver the
13432 * optimum resolution. The MJD method and the date & time methods
13433 * are both good compromises between resolution and convenience.
13434 *
13435 * <li> The nutation components in longitude and obliquity are in radians
13436 * and with respect to the mean equinox and ecliptic of date,
13437 * IAU 2006 precession model (Hilton et al. 2006, Capitaine et al.
13438 * 2005).
13439 *
13440 * <li> The function first computes the IAU 2000A nutation, then applies
13441 * adjustments for (i) the consequences of the change in obliquity
13442 * from the IAU 1980 ecliptic to the IAU 2006 ecliptic and (ii) the
13443 * secular variation in the Earth's dynamical flattening.
13444 *
13445 * <li> The present function provides classical nutation, complementing
13446 * the IAU 2000 frame bias and IAU 2006 precession. It delivers a
13447 * pole which is at current epochs accurate to a few tens of
13448 * microarcseconds, apart from the free core nutation.
13449 *</ol>
13450 *<p>Called:<ul>
13451 * <li>{@link #jauNut00a} nutation, IAU 2000A
13452 * </ul>
13453 *<p>References:
13454 *
13455 * <p>Chapront, J., Chapront-Touze, M. & Francou, G. 2002,
13456 * Astron.Astrophys. 387, 700
13457 *
13458 * <p>Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977,
13459 * Astron.Astrophys. 58, 1-16
13460 *
13461 * <p>Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res.
13462 * 107, B4. The MHB_2000 code itself was obtained on 9th September
13463 * 2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
13464 *
13465 * <p>Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
13466 * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
13467 *
13468 * <p>Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
13469 * Astron.Astrophys.Supp.Ser. 135, 111
13470 *
13471 * <p>Wallace, P.T., "Software for Implementing the IAU 2000
13472 * Resolutions", in IERS Workshop 5.1 (2002)
13473 *
13474 *@version 2008 May 24
13475 *
13476 * @since Release 20101201
13477 *
13478 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
13479 */
13480 public static NutationTerms jauNut06a(double date1, double date2)
13481 {
13482 double t, fj2;
13483
13484
13485 /* Interval between fundamental date J2000.0 and given date (JC). */
13486 t = ((date1 - DJ00) + date2) / DJC;
13487
13488 /* Factor correcting for secular variation of J2. */
13489 fj2 = -2.7774e-6 * t;
13490
13491 /* Obtain IAU 2000A nutation. */
13492 NutationTerms nt = jauNut00a(date1, date2);
13493
13494 /* Apply P03 adjustments (Wallace & Capitaine, 2006, Eqs.5). */
13495 return new NutationTerms( nt.dpsi + nt.dpsi * (0.4697e-6 + fj2),
13496 nt.deps + nt.deps * fj2);
13497
13498 }
13499
13500 /**
13501 * Nutation, IAU 1980 model.
13502 *
13503 *<p>This function is derived from the International Astronomical Union's
13504 * SOFA (Standards Of Fundamental Astronomy) software collection.
13505 *
13506 *<p>Status: canonical model.
13507 *
13508 *<!-- Given: -->
13509 * @param date1 double TT as a 2-part Julian Date (Note 1)
13510 * @param date2 double TT as a 2-part Julian Date (Note 1)
13511 *
13512 *<!-- Returned: -->
13513 * @return dpsi double <u>returned</u> nutation in longitude (radians)
13514 * deps double <u>returned</u> nutation in obliquity (radians)
13515 *
13516 * <p>Notes:
13517 * <ol>
13518 *
13519 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
13520 * convenient way between the two arguments. For example,
13521 * JD(TT)=2450123.7 could be expressed in any of these ways,
13522 * among others:
13523 *<pre>
13524 * date1 date2
13525 *
13526 * 2450123.7 0.0 (JD method)
13527 * 2451545.0 -1421.3 (J2000 method)
13528 * 2400000.5 50123.2 (MJD method)
13529 * 2450123.5 0.2 (date & time method)
13530 *</pre>
13531 * The JD method is the most natural and convenient to use in
13532 * cases where the loss of several decimal digits of resolution
13533 * is acceptable. The J2000 method is best matched to the way
13534 * the argument is handled internally and will deliver the
13535 * optimum resolution. The MJD method and the date & time methods
13536 * are both good compromises between resolution and convenience.
13537 *
13538 * <li> The nutation components are with respect to the ecliptic of
13539 * date.
13540 *</ol>
13541 *<p>Called:<ul>
13542 * <li>{@link #jauAnpm} normalize angle into range +/- pi
13543 * </ul>
13544 *<p>Reference:
13545 *
13546 * <p>Explanatory Supplement to the Astronomical Almanac,
13547 * P. Kenneth Seidelmann (ed), University Science Books (1992),
13548 * Section 3.222 (p111).
13549 *
13550 *@version 2008 September 30
13551 *
13552 * @since Release 20101201
13553 *
13554 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
13555 */
13556 public static NutationTerms jauNut80(double date1, double date2)
13557 {
13558 double t, el, elp, f, d, om, dp, de, arg, s, c;
13559 int j;
13560
13561 /* Units of 0.1 milliarcsecond to radians */
13562 final double U2R = DAS2R / 1e4;
13563
13564 /* ------------------------------------------------ */
13565 /* Table of multiples of arguments and coefficients */
13566 /* ------------------------------------------------ */
13567
13568 /* The units for the sine and cosine coefficients are 0.1 mas and */
13569 /* the same per Julian century */
13570
13571 final class NutationModel {
13572 final int nl,nlp,nf,nd,nom; /* coefficients of l,l',F,D,Om */
13573 final double sp,spt; /* longitude sine, 1 and t coefficients */
13574 final double ce,cet; /* obliquity cosine, 1 and t coefficients */
13575
13576 public NutationModel(int nl,int nlp,int nf,int nd,int nom,
13577 double sp,double spt,
13578 double ce,double cet ) {
13579 this.nl = nl;this.nlp = nlp;this.nf = nf;this.nd = nd;this.nom = nom;
13580 this.sp = sp;this.spt = spt;
13581 this.ce = ce;this.cet = cet;
13582 }
13583 }
13584 NutationModel x[] = {
13585
13586 /* 1-10 */
13587 new NutationModel( 0, 0, 0, 0, 1, -171996.0, -174.2, 92025.0, 8.9 ),
13588 new NutationModel( 0, 0, 0, 0, 2, 2062.0, 0.2, -895.0, 0.5 ),
13589 new NutationModel( -2, 0, 2, 0, 1, 46.0, 0.0, -24.0, 0.0 ),
13590 new NutationModel( 2, 0, -2, 0, 0, 11.0, 0.0, 0.0, 0.0 ),
13591 new NutationModel( -2, 0, 2, 0, 2, -3.0, 0.0, 1.0, 0.0 ),
13592 new NutationModel( 1, -1, 0, -1, 0, -3.0, 0.0, 0.0, 0.0 ),
13593 new NutationModel( 0, -2, 2, -2, 1, -2.0, 0.0, 1.0, 0.0 ),
13594 new NutationModel( 2, 0, -2, 0, 1, 1.0, 0.0, 0.0, 0.0 ),
13595 new NutationModel( 0, 0, 2, -2, 2, -13187.0, -1.6, 5736.0, -3.1 ),
13596 new NutationModel( 0, 1, 0, 0, 0, 1426.0, -3.4, 54.0, -0.1 ),
13597
13598 /* 11-20 */
13599 new NutationModel( 0, 1, 2, -2, 2, -517.0, 1.2, 224.0, -0.6 ),
13600 new NutationModel( 0, -1, 2, -2, 2, 217.0, -0.5, -95.0, 0.3 ),
13601 new NutationModel( 0, 0, 2, -2, 1, 129.0, 0.1, -70.0, 0.0 ),
13602 new NutationModel( 2, 0, 0, -2, 0, 48.0, 0.0, 1.0, 0.0 ),
13603 new NutationModel( 0, 0, 2, -2, 0, -22.0, 0.0, 0.0, 0.0 ),
13604 new NutationModel( 0, 2, 0, 0, 0, 17.0, -0.1, 0.0, 0.0 ),
13605 new NutationModel( 0, 1, 0, 0, 1, -15.0, 0.0, 9.0, 0.0 ),
13606 new NutationModel( 0, 2, 2, -2, 2, -16.0, 0.1, 7.0, 0.0 ),
13607 new NutationModel( 0, -1, 0, 0, 1, -12.0, 0.0, 6.0, 0.0 ),
13608 new NutationModel( -2, 0, 0, 2, 1, -6.0, 0.0, 3.0, 0.0 ),
13609
13610 /* 21-30 */
13611 new NutationModel( 0, -1, 2, -2, 1, -5.0, 0.0, 3.0, 0.0 ),
13612 new NutationModel( 2, 0, 0, -2, 1, 4.0, 0.0, -2.0, 0.0 ),
13613 new NutationModel( 0, 1, 2, -2, 1, 4.0, 0.0, -2.0, 0.0 ),
13614 new NutationModel( 1, 0, 0, -1, 0, -4.0, 0.0, 0.0, 0.0 ),
13615 new NutationModel( 2, 1, 0, -2, 0, 1.0, 0.0, 0.0, 0.0 ),
13616 new NutationModel( 0, 0, -2, 2, 1, 1.0, 0.0, 0.0, 0.0 ),
13617 new NutationModel( 0, 1, -2, 2, 0, -1.0, 0.0, 0.0, 0.0 ),
13618 new NutationModel( 0, 1, 0, 0, 2, 1.0, 0.0, 0.0, 0.0 ),
13619 new NutationModel( -1, 0, 0, 1, 1, 1.0, 0.0, 0.0, 0.0 ),
13620 new NutationModel( 0, 1, 2, -2, 0, -1.0, 0.0, 0.0, 0.0 ),
13621
13622 /* 31-40 */
13623 new NutationModel( 0, 0, 2, 0, 2, -2274.0, -0.2, 977.0, -0.5 ),
13624 new NutationModel( 1, 0, 0, 0, 0, 712.0, 0.1, -7.0, 0.0 ),
13625 new NutationModel( 0, 0, 2, 0, 1, -386.0, -0.4, 200.0, 0.0 ),
13626 new NutationModel( 1, 0, 2, 0, 2, -301.0, 0.0, 129.0, -0.1 ),
13627 new NutationModel( 1, 0, 0, -2, 0, -158.0, 0.0, -1.0, 0.0 ),
13628 new NutationModel( -1, 0, 2, 0, 2, 123.0, 0.0, -53.0, 0.0 ),
13629 new NutationModel( 0, 0, 0, 2, 0, 63.0, 0.0, -2.0, 0.0 ),
13630 new NutationModel( 1, 0, 0, 0, 1, 63.0, 0.1, -33.0, 0.0 ),
13631 new NutationModel( -1, 0, 0, 0, 1, -58.0, -0.1, 32.0, 0.0 ),
13632 new NutationModel( -1, 0, 2, 2, 2, -59.0, 0.0, 26.0, 0.0 ),
13633
13634 /* 41-50 */
13635 new NutationModel( 1, 0, 2, 0, 1, -51.0, 0.0, 27.0, 0.0 ),
13636 new NutationModel( 0, 0, 2, 2, 2, -38.0, 0.0, 16.0, 0.0 ),
13637 new NutationModel( 2, 0, 0, 0, 0, 29.0, 0.0, -1.0, 0.0 ),
13638 new NutationModel( 1, 0, 2, -2, 2, 29.0, 0.0, -12.0, 0.0 ),
13639 new NutationModel( 2, 0, 2, 0, 2, -31.0, 0.0, 13.0, 0.0 ),
13640 new NutationModel( 0, 0, 2, 0, 0, 26.0, 0.0, -1.0, 0.0 ),
13641 new NutationModel( -1, 0, 2, 0, 1, 21.0, 0.0, -10.0, 0.0 ),
13642 new NutationModel( -1, 0, 0, 2, 1, 16.0, 0.0, -8.0, 0.0 ),
13643 new NutationModel( 1, 0, 0, -2, 1, -13.0, 0.0, 7.0, 0.0 ),
13644 new NutationModel( -1, 0, 2, 2, 1, -10.0, 0.0, 5.0, 0.0 ),
13645
13646 /* 51-60 */
13647 new NutationModel( 1, 1, 0, -2, 0, -7.0, 0.0, 0.0, 0.0 ),
13648 new NutationModel( 0, 1, 2, 0, 2, 7.0, 0.0, -3.0, 0.0 ),
13649 new NutationModel( 0, -1, 2, 0, 2, -7.0, 0.0, 3.0, 0.0 ),
13650 new NutationModel( 1, 0, 2, 2, 2, -8.0, 0.0, 3.0, 0.0 ),
13651 new NutationModel( 1, 0, 0, 2, 0, 6.0, 0.0, 0.0, 0.0 ),
13652 new NutationModel( 2, 0, 2, -2, 2, 6.0, 0.0, -3.0, 0.0 ),
13653 new NutationModel( 0, 0, 0, 2, 1, -6.0, 0.0, 3.0, 0.0 ),
13654 new NutationModel( 0, 0, 2, 2, 1, -7.0, 0.0, 3.0, 0.0 ),
13655 new NutationModel( 1, 0, 2, -2, 1, 6.0, 0.0, -3.0, 0.0 ),
13656 new NutationModel( 0, 0, 0, -2, 1, -5.0, 0.0, 3.0, 0.0 ),
13657
13658 /* 61-70 */
13659 new NutationModel( 1, -1, 0, 0, 0, 5.0, 0.0, 0.0, 0.0 ),
13660 new NutationModel( 2, 0, 2, 0, 1, -5.0, 0.0, 3.0, 0.0 ),
13661 new NutationModel( 0, 1, 0, -2, 0, -4.0, 0.0, 0.0, 0.0 ),
13662 new NutationModel( 1, 0, -2, 0, 0, 4.0, 0.0, 0.0, 0.0 ),
13663 new NutationModel( 0, 0, 0, 1, 0, -4.0, 0.0, 0.0, 0.0 ),
13664 new NutationModel( 1, 1, 0, 0, 0, -3.0, 0.0, 0.0, 0.0 ),
13665 new NutationModel( 1, 0, 2, 0, 0, 3.0, 0.0, 0.0, 0.0 ),
13666 new NutationModel( 1, -1, 2, 0, 2, -3.0, 0.0, 1.0, 0.0 ),
13667 new NutationModel( -1, -1, 2, 2, 2, -3.0, 0.0, 1.0, 0.0 ),
13668 new NutationModel( -2, 0, 0, 0, 1, -2.0, 0.0, 1.0, 0.0 ),
13669
13670 /* 71-80 */
13671 new NutationModel( 3, 0, 2, 0, 2, -3.0, 0.0, 1.0, 0.0 ),
13672 new NutationModel( 0, -1, 2, 2, 2, -3.0, 0.0, 1.0, 0.0 ),
13673 new NutationModel( 1, 1, 2, 0, 2, 2.0, 0.0, -1.0, 0.0 ),
13674 new NutationModel( -1, 0, 2, -2, 1, -2.0, 0.0, 1.0, 0.0 ),
13675 new NutationModel( 2, 0, 0, 0, 1, 2.0, 0.0, -1.0, 0.0 ),
13676 new NutationModel( 1, 0, 0, 0, 2, -2.0, 0.0, 1.0, 0.0 ),
13677 new NutationModel( 3, 0, 0, 0, 0, 2.0, 0.0, 0.0, 0.0 ),
13678 new NutationModel( 0, 0, 2, 1, 2, 2.0, 0.0, -1.0, 0.0 ),
13679 new NutationModel( -1, 0, 0, 0, 2, 1.0, 0.0, -1.0, 0.0 ),
13680 new NutationModel( 1, 0, 0, -4, 0, -1.0, 0.0, 0.0, 0.0 ),
13681
13682 /* 81-90 */
13683 new NutationModel( -2, 0, 2, 2, 2, 1.0, 0.0, -1.0, 0.0 ),
13684 new NutationModel( -1, 0, 2, 4, 2, -2.0, 0.0, 1.0, 0.0 ),
13685 new NutationModel( 2, 0, 0, -4, 0, -1.0, 0.0, 0.0, 0.0 ),
13686 new NutationModel( 1, 1, 2, -2, 2, 1.0, 0.0, -1.0, 0.0 ),
13687 new NutationModel( 1, 0, 2, 2, 1, -1.0, 0.0, 1.0, 0.0 ),
13688 new NutationModel( -2, 0, 2, 4, 2, -1.0, 0.0, 1.0, 0.0 ),
13689 new NutationModel( -1, 0, 4, 0, 2, 1.0, 0.0, 0.0, 0.0 ),
13690 new NutationModel( 1, -1, 0, -2, 0, 1.0, 0.0, 0.0, 0.0 ),
13691 new NutationModel( 2, 0, 2, -2, 1, 1.0, 0.0, -1.0, 0.0 ),
13692 new NutationModel( 2, 0, 2, 2, 2, -1.0, 0.0, 0.0, 0.0 ),
13693
13694 /* 91-100 */
13695 new NutationModel( 1, 0, 0, 2, 1, -1.0, 0.0, 0.0, 0.0 ),
13696 new NutationModel( 0, 0, 4, -2, 2, 1.0, 0.0, 0.0, 0.0 ),
13697 new NutationModel( 3, 0, 2, -2, 2, 1.0, 0.0, 0.0, 0.0 ),
13698 new NutationModel( 1, 0, 2, -2, 0, -1.0, 0.0, 0.0, 0.0 ),
13699 new NutationModel( 0, 1, 2, 0, 1, 1.0, 0.0, 0.0, 0.0 ),
13700 new NutationModel( -1, -1, 0, 2, 1, 1.0, 0.0, 0.0, 0.0 ),
13701 new NutationModel( 0, 0, -2, 0, 1, -1.0, 0.0, 0.0, 0.0 ),
13702 new NutationModel( 0, 0, 2, -1, 2, -1.0, 0.0, 0.0, 0.0 ),
13703 new NutationModel( 0, 1, 0, 2, 0, -1.0, 0.0, 0.0, 0.0 ),
13704 new NutationModel( 1, 0, -2, -2, 0, -1.0, 0.0, 0.0, 0.0 ),
13705
13706 /* 101-106 */
13707 new NutationModel( 0, -1, 2, 0, 1, -1.0, 0.0, 0.0, 0.0 ),
13708 new NutationModel( 1, 1, 0, -2, 1, -1.0, 0.0, 0.0, 0.0 ),
13709 new NutationModel( 1, 0, -2, 2, 0, -1.0, 0.0, 0.0, 0.0 ),
13710 new NutationModel( 2, 0, 0, 2, 0, 1.0, 0.0, 0.0, 0.0 ),
13711 new NutationModel( 0, 0, 2, 4, 2, -1.0, 0.0, 0.0, 0.0 ),
13712 new NutationModel( 0, 1, 0, 1, 0, 1.0, 0.0, 0.0, 0.0 )
13713 };
13714
13715 /* Number of terms in the series */
13716 final int NT = x.length;
13717
13718 /*--------------------------------------------------------------------*/
13719
13720 /* Interval between fundamental epoch J2000.0 and given date (JC). */
13721 t = ((date1 - DJ00) + date2) / DJC;
13722
13723 /* --------------------- */
13724 /* Fundamental arguments */
13725 /* --------------------- */
13726
13727 /* Mean longitude of Moon minus mean longitude of Moon's perigee. */
13728 el = jauAnpm(
13729 (485866.733 + (715922.633 + (31.310 + 0.064 * t) * t) * t)
13730 * DAS2R + fmod(1325.0 * t, 1.0) * D2PI);
13731
13732 /* Mean longitude of Sun minus mean longitude of Sun's perigee. */
13733 elp = jauAnpm(
13734 (1287099.804 + (1292581.224 + (-0.577 - 0.012 * t) * t) * t)
13735 * DAS2R + fmod(99.0 * t, 1.0) * D2PI);
13736
13737 /* Mean longitude of Moon minus mean longitude of Moon's node. */
13738 f = jauAnpm(
13739 (335778.877 + (295263.137 + (-13.257 + 0.011 * t) * t) * t)
13740 * DAS2R + fmod(1342.0 * t, 1.0) * D2PI);
13741
13742 /* Mean elongation of Moon from Sun. */
13743 d = jauAnpm(
13744 (1072261.307 + (1105601.328 + (-6.891 + 0.019 * t) * t) * t)
13745 * DAS2R + fmod(1236.0 * t, 1.0) * D2PI);
13746
13747 /* Longitude of the mean ascending node of the lunar orbit on the */
13748 /* ecliptic, measured from the mean equinox of date. */
13749 om = jauAnpm(
13750 (450160.280 + (-482890.539 + (7.455 + 0.008 * t) * t) * t)
13751 * DAS2R + fmod(-5.0 * t, 1.0) * D2PI);
13752
13753 /* --------------- */
13754 /* Nutation series */
13755 /* --------------- */
13756
13757 /* Initialize nutation components. */
13758 dp = 0.0;
13759 de = 0.0;
13760
13761 /* Sum the nutation terms, ending with the biggest. */
13762 for (j = NT-1; j >= 0; j--) {
13763
13764 /* Form argument for current term. */
13765 arg = (double)x[j].nl * el
13766 + (double)x[j].nlp * elp
13767 + (double)x[j].nf * f
13768 + (double)x[j].nd * d
13769 + (double)x[j].nom * om;
13770
13771 /* Accumulate current nutation term. */
13772 s = x[j].sp + x[j].spt * t;
13773 c = x[j].ce + x[j].cet * t;
13774 if (s != 0.0) dp += s * sin(arg);
13775 if (c != 0.0) de += c * cos(arg);
13776 }
13777
13778 /* Convert results from 0.1 mas units to radians. */
13779 return new NutationTerms( dp * U2R,
13780 de * U2R);
13781
13782 }
13783
13784
13785 /**
13786 * Form the matrix of nutation for a given date, IAU 1980 model.
13787 *
13788 *<p>This function is derived from the International Astronomical Union's
13789 * SOFA (Standards Of Fundamental Astronomy) software collection.
13790 *
13791 *<p>Status: support function.
13792 *
13793 *<!-- Given: -->
13794 * @param date1 double TDB date (Note 1)
13795 * @param date2 double TDB date (Note 1)
13796 *
13797 *<!-- Returned: -->
13798 * @return double[3][3] nutation matrix
13799 *
13800 * <p>Notes:
13801 * <ol>
13802 *
13803 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
13804 * convenient way between the two arguments. For example,
13805 * JD(TT)=2450123.7 could be expressed in any of these ways,
13806 * among others:
13807 *<pre>
13808 * date1 date2
13809 *
13810 * 2450123.7 0.0 (JD method)
13811 * 2451545.0 -1421.3 (J2000 method)
13812 * 2400000.5 50123.2 (MJD method)
13813 * 2450123.5 0.2 (date & time method)
13814 *</pre>
13815 * The JD method is the most natural and convenient to use in
13816 * cases where the loss of several decimal digits of resolution
13817 * is acceptable. The J2000 method is best matched to the way
13818 * the argument is handled internally and will deliver the
13819 * optimum resolution. The MJD method and the date & time methods
13820 * are both good compromises between resolution and convenience.
13821 *
13822 * <li> The matrix operates in the sense V(true) = rmatn * V(mean),
13823 * where the p-vector V(true) is with respect to the true
13824 * equatorial triad of date and the p-vector V(mean) is with
13825 * respect to the mean equatorial triad of date.
13826 *</ol>
13827 *<p>Called:<ul>
13828 * <li>{@link #jauNut80} nutation, IAU 1980
13829 * <li>{@link #jauObl80} mean obliquity, IAU 1980
13830 * <li>{@link #jauNumat} form nutation matrix
13831 * </ul>
13832 *@version 2008 May 12
13833 *
13834 * @since Release 20101201
13835 *
13836 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
13837 */
13838 public static double[][] jauNutm80(double date1, double date2)
13839 {
13840 double rmatn[][];
13841 /* Nutation components and mean obliquity. */
13842 NutationTerms nt = jauNut80(date1, date2);
13843 double epsa = jauObl80(date1, date2);
13844
13845 /* Build the rotation matrix. */
13846 rmatn = jauNumat(epsa, nt.dpsi, nt.deps);
13847
13848 return rmatn;
13849
13850 }
13851
13852
13853 /**
13854 * Mean obliquity of the ecliptic, IAU 2006 precession model.
13855 *
13856 *<p>This function is derived from the International Astronomical Union's
13857 * SOFA (Standards Of Fundamental Astronomy) software collection.
13858 *
13859 *<p>Status: canonical model.
13860 *
13861 *<!-- Given: -->
13862 * @param date1 double TT as a 2-part Julian Date (Note 1)
13863 * @param date2 double TT as a 2-part Julian Date (Note 1)
13864 *
13865 * <!-- Returned (function value): -->
13866 * @return double obliquity of the ecliptic (radians, Note 2)
13867 *
13868 * <p>Notes:
13869 * <ol>
13870 *
13871 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
13872 * convenient way between the two arguments. For example,
13873 * JD(TT)=2450123.7 could be expressed in any of these ways,
13874 * among others:
13875 *<pre>
13876 * date1 date2
13877 *
13878 * 2450123.7 0.0 (JD method)
13879 * 2451545.0 -1421.3 (J2000 method)
13880 * 2400000.5 50123.2 (MJD method)
13881 * 2450123.5 0.2 (date & time method)
13882 *</pre>
13883 * The JD method is the most natural and convenient to use in
13884 * cases where the loss of several decimal digits of resolution
13885 * is acceptable. The J2000 method is best matched to the way
13886 * the argument is handled internally and will deliver the
13887 * optimum resolution. The MJD method and the date & time methods
13888 * are both good compromises between resolution and convenience.
13889 *
13890 * <li> The result is the angle between the ecliptic and mean equator of
13891 * date date1+date2.
13892 *</ol>
13893 *<p>Reference:
13894 *
13895 * Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
13896 *
13897 *@version 2009 March 16
13898 *
13899 * @since Release 20101201
13900 *
13901 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
13902 */
13903 public static double jauObl06(double date1, double date2)
13904 {
13905 double t, eps0;
13906
13907
13908 /* Interval between fundamental date J2000.0 and given date (JC). */
13909 t = ((date1 - DJ00) + date2) / DJC;
13910
13911 /* Mean obliquity. */
13912 eps0 = (84381.406 +
13913 (-46.836769 +
13914 ( -0.0001831 +
13915 ( 0.00200340 +
13916 ( -0.000000576 +
13917 ( -0.0000000434) * t) * t) * t) * t) * t) * DAS2R;
13918
13919 return eps0;
13920
13921 }
13922
13923
13924 /**
13925 * Mean obliquity of the ecliptic, IAU 1980 model.
13926 *
13927 *<p>This function is derived from the International Astronomical Union's
13928 * SOFA (Standards Of Fundamental Astronomy) software collection.
13929 *
13930 *<p>Status: canonical model.
13931 *
13932 *<!-- Given: -->
13933 * @param date1 double TT as a 2-part Julian Date (Note 1)
13934 * @param date2 double TT as a 2-part Julian Date (Note 1)
13935 *
13936 * <!-- Returned (function value): -->
13937 * @return double obliquity of the ecliptic (radians, Note 2)
13938 *
13939 * <p>Notes:
13940 * <ol>
13941 *
13942 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
13943 * convenient way between the two arguments. For example,
13944 * JD(TT)=2450123.7 could be expressed in any of these ways,
13945 * among others:
13946 *<pre>
13947 * date1 date2
13948 *
13949 * 2450123.7 0.0 (JD method)
13950 * 2451545.0 -1421.3 (J2000 method)
13951 * 2400000.5 50123.2 (MJD method)
13952 * 2450123.5 0.2 (date & time method)
13953 *</pre>
13954 * The JD method is the most natural and convenient to use in
13955 * cases where the loss of several decimal digits of resolution
13956 * is acceptable. The J2000 method is best matched to the way
13957 * the argument is handled internally and will deliver the
13958 * optimum resolution. The MJD method and the date & time methods
13959 * are both good compromises between resolution and convenience.
13960 *
13961 * <li> The result is the angle between the ecliptic and mean equator of
13962 * date date1+date2.
13963 *</ol>
13964 *<p>Reference:
13965 *
13966 * <p>Explanatory Supplement to the Astronomical Almanac,
13967 * P. Kenneth Seidelmann (ed), University Science Books (1992),
13968 * Expression 3.222-1 (p114).
13969 *
13970 *@version 2009 March 16
13971 *
13972 * @since Release 20101201
13973 *
13974 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
13975 */
13976 public static double jauObl80(double date1, double date2)
13977 {
13978 double t, eps0;
13979
13980
13981 /* Interval between fundamental epoch J2000.0 and given date (JC). */
13982 t = ((date1 - DJ00) + date2) / DJC;
13983
13984 /* Mean obliquity of date. */
13985 eps0 = DAS2R * (84381.448 +
13986 (-46.8150 +
13987 (-0.00059 +
13988 ( 0.001813) * t) * t) * t);
13989
13990 return eps0;
13991
13992 }
13993
13994
13995 /**
13996 * equinox based precession angles.
13997 * .
13998 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 21 Nov 2011
13999 * @version $Revision$ $date$
14000 */
14001 public static class PrecessionAngles {
14002 /** epsilon_0 obliquity at J2000.0. */
14003 public double eps0;
14004 /** psi_A luni-solar precession. */
14005 public double psia;
14006 /** omega_A inclination of equator wrt J2000.0 ecliptic. */
14007 public double oma;
14008 /** P_A ecliptic pole x, J2000.0 ecliptic triad. */
14009 public double bpa;
14010 /** Q_A ecliptic pole -y, J2000.0 ecliptic triad. */
14011 public double bqa;
14012 /** pi_A angle between moving and J2000.0 ecliptics. */
14013 public double pia;
14014 /** Pi_A longitude of ascending node of the ecliptic. */
14015 public double bpia;
14016 /** epsilon_A obliquity of the ecliptic. */
14017 public double epsa;
14018 /** chi_A planetary precession. */
14019 public double chia;
14020 /** z_A equatorial precession: -3rd 323 Euler angle. */
14021 public double za;
14022 /** zeta_A equatorial precession: -1st 323 Euler angle. */
14023 public double zetaa;
14024 /** theta_A equatorial precession: 2nd 323 Euler angle. */
14025 public double thetaa;
14026 /** p_A general precession. */
14027 public double pa;
14028 /** gamma_J2000 J2000.0 RA difference of ecliptic poles. */
14029 public double gam;
14030 /** phi_J2000 J2000.0 codeclination of ecliptic pole. */
14031 public double phi;
14032 /** psi_J2000 longitude difference of equator poles, J2000.0. */
14033 public double psi;
14034
14035 public PrecessionAngles ( double eps0, double psia, double oma, double bpa,
14036 double bqa, double pia, double bpia,
14037 double epsa, double chia, double za, double zetaa,
14038 double thetaa, double pa,
14039 double gam, double phi, double psi){
14040
14041 this.eps0 = eps0;
14042 this.psia = psia;
14043 this.oma = oma;
14044 this.bpa = bpa;
14045 this.bqa = bqa;
14046 this.pia = pia;
14047 this.bpia = bpia;
14048 this.epsa = epsa;
14049 this.chia = chia;
14050 this.za = za;
14051 this.zetaa = zetaa;
14052 this.thetaa = thetaa;
14053 this.pa = pa;
14054 this.gam = gam;
14055 this.phi = phi;
14056 this.psi = psi;
14057 }
14058 }
14059 /**
14060 * Precession angles, IAU 2006, equinox based.
14061 *
14062 *<p>This function is derived from the International Astronomical Union's
14063 * SOFA (Standards Of Fundamental Astronomy) software collection.
14064 *
14065 *<p>Status: canonical models.
14066 *
14067 *<!-- Given: -->
14068 * @param date1 double TT as a 2-part Julian Date (Note 1)
14069 * @param date2 double TT as a 2-part Julian Date (Note 1)
14070 *
14071 * Returned (see Note 2):
14072 * eps0 double epsilon_0
14073 * psia double psi_A
14074 * oma double omega_A
14075 * bpa double P_A
14076 * bqa double Q_A
14077 * pia double pi_A
14078 * bpia double Pi_A
14079 * epsa double obliquity epsilon_A
14080 * chia double chi_A
14081 * za double z_A
14082 * zetaa double zeta_A
14083 * thetaa double theta_A
14084 * pa double p_A
14085 * gam double F-W angle gamma_J2000
14086 * phi double F-W angle phi_J2000
14087 * psi double F-W angle psi_J2000
14088 *
14089 * <p>Notes:
14090 * <ol>
14091 *
14092 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
14093 * convenient way between the two arguments. For example,
14094 * JD(TT)=2450123.7 could be expressed in any of these ways,
14095 * among others:
14096 *<pre>
14097 * date1 date2
14098 *
14099 * 2450123.7 0.0 (JD method)
14100 * 2451545.0 -1421.3 (J2000 method)
14101 * 2400000.5 50123.2 (MJD method)
14102 * 2450123.5 0.2 (date & time method)
14103 *</pre>
14104 * The JD method is the most natural and convenient to use in
14105 * cases where the loss of several decimal digits of resolution
14106 * is acceptable. The J2000 method is best matched to the way
14107 * the argument is handled internally and will deliver the
14108 * optimum resolution. The MJD method and the date & time methods
14109 * are both good compromises between resolution and convenience.
14110 *
14111 * <li> This function returns the set of equinox based angles for the
14112 * Capitaine et al. "P03" precession theory, adopted by the IAU in
14113 * 2006. The angles are set out in Table 1 of Hilton et al. (2006):
14114 *
14115 * eps0 epsilon_0 obliquity at J2000.0
14116 * psia psi_A luni-solar precession
14117 * oma omega_A inclination of equator wrt J2000.0 ecliptic
14118 * bpa P_A ecliptic pole x, J2000.0 ecliptic triad
14119 * bqa Q_A ecliptic pole -y, J2000.0 ecliptic triad
14120 * pia pi_A angle between moving and J2000.0 ecliptics
14121 * bpia Pi_A longitude of ascending node of the ecliptic
14122 * epsa epsilon_A obliquity of the ecliptic
14123 * chia chi_A planetary precession
14124 * za z_A equatorial precession: -3rd 323 Euler angle
14125 * zetaa zeta_A equatorial precession: -1st 323 Euler angle
14126 * thetaa theta_A equatorial precession: 2nd 323 Euler angle
14127 * pa p_A general precession
14128 * gam gamma_J2000 J2000.0 RA difference of ecliptic poles
14129 * phi phi_J2000 J2000.0 codeclination of ecliptic pole
14130 * psi psi_J2000 longitude difference of equator poles, J2000.0
14131 *
14132 * The returned values are all radians.
14133 *
14134 * <li> Hilton et al. (2006) Table 1 also contains angles that depend on
14135 * models distinct from the P03 precession theory itself, namely the
14136 * IAU 2000A frame bias and nutation. The quoted polynomials are
14137 * used in other JSOFA functions:
14138 *
14139 * . jauXy06 contains the polynomial parts of the X and Y series.
14140 *
14141 * . jauS06 contains the polynomial part of the s+XY/2 series.
14142 *
14143 * . jauPfw06 implements the series for the Fukushima-Williams
14144 * angles that are with respect to the GCRS pole (i.e. the variants
14145 * that include frame bias).
14146 *
14147 * <li> The IAU resolution stipulated that the choice of parameterization
14148 * was left to the user, and so an IAU compliant precession
14149 * implementation can be constructed using various combinations of
14150 * the angles returned by the present function.
14151 *
14152 * <li> The parameterization used by JSOFA is the Fukushima-Williams angles
14153 * referred directly to the GCRS pole. These are the final four
14154 * arguments returned by the present function, but are more
14155 * efficiently calculated by calling the function jauPfw06. JSOFA
14156 * also supports the direct computation of the CIP GCRS X,Y by
14157 * series, available by calling jauXy06.
14158 *
14159 * <li> The agreement between the different parameterizations is at the
14160 * 1 microarcsecond level in the present era.
14161 *
14162 * <li> When constructing a precession formulation that refers to the GCRS
14163 * pole rather than the dynamical pole, it may (depending on the
14164 * choice of angles) be necessary to introduce the frame bias
14165 * explicitly.
14166 *
14167 * <li> It is permissible to re-use the same variable in the returned
14168 * arguments. The quantities are stored in the stated order.
14169 *</ol>
14170 *<p>Reference:
14171 *
14172 * Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
14173 *
14174 *<p>Called:<ul>
14175 * <li>{@link #jauObl06} mean obliquity, IAU 2006
14176 * </ul>
14177 *@version 2009 December 17
14178 *
14179 * @since Release 20101201
14180 *
14181 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
14182 */
14183 public static PrecessionAngles jauP06e(double date1, double date2)
14184 {
14185 double t;
14186 double eps0, psia, oma, bpa,
14187 bqa, pia, bpia,
14188 epsa, chia, za, zetaa,
14189 thetaa, pa,
14190 gam, phi, psi;
14191
14192 /* Interval between fundamental date J2000.0 and given date (JC). */
14193 t = ((date1 - DJ00) + date2) / DJC;
14194
14195 /* Obliquity at J2000.0. */
14196
14197 eps0 = 84381.406 * DAS2R;
14198
14199 /* Luni-solar precession. */
14200
14201 psia = ( 5038.481507 +
14202 ( -1.0790069 +
14203 ( -0.00114045 +
14204 ( 0.000132851 +
14205 ( -0.0000000951 )
14206 * t) * t) * t) * t) * t * DAS2R;
14207
14208 /* Inclination of mean equator with respect to the J2000.0 ecliptic. */
14209
14210 oma = eps0 + ( -0.025754 +
14211 ( 0.0512623 +
14212 ( -0.00772503 +
14213 ( -0.000000467 +
14214 ( 0.0000003337 )
14215 * t) * t) * t) * t) * t * DAS2R;
14216
14217 /* Ecliptic pole x, J2000.0 ecliptic triad. */
14218
14219 bpa = ( 4.199094 +
14220 ( 0.1939873 +
14221 ( -0.00022466 +
14222 ( -0.000000912 +
14223 ( 0.0000000120 )
14224 * t) * t) * t) * t) * t * DAS2R;
14225
14226 /* Ecliptic pole -y, J2000.0 ecliptic triad. */
14227
14228 bqa = ( -46.811015 +
14229 ( 0.0510283 +
14230 ( 0.00052413 +
14231 ( -0.000000646 +
14232 ( -0.0000000172 )
14233 * t) * t) * t) * t) * t * DAS2R;
14234
14235 /* Angle between moving and J2000.0 ecliptics. */
14236
14237 pia = ( 46.998973 +
14238 ( -0.0334926 +
14239 ( -0.00012559 +
14240 ( 0.000000113 +
14241 ( -0.0000000022 )
14242 * t) * t) * t) * t) * t * DAS2R;
14243
14244 /* Longitude of ascending node of the moving ecliptic. */
14245
14246 bpia = ( 629546.7936 +
14247 ( -867.95758 +
14248 ( 0.157992 +
14249 ( -0.0005371 +
14250 ( -0.00004797 +
14251 ( 0.000000072 )
14252 * t) * t) * t) * t) * t) * DAS2R;
14253
14254 /* Mean obliquity of the ecliptic. */
14255
14256 epsa = jauObl06(date1, date2);
14257
14258 /* Planetary precession. */
14259
14260 chia = ( 10.556403 +
14261 ( -2.3814292 +
14262 ( -0.00121197 +
14263 ( 0.000170663 +
14264 ( -0.0000000560 )
14265 * t) * t) * t) * t) * t * DAS2R;
14266
14267 /* Equatorial precession: minus the third of the 323 Euler angles. */
14268
14269 za = ( -2.650545 +
14270 ( 2306.077181 +
14271 ( 1.0927348 +
14272 ( 0.01826837 +
14273 ( -0.000028596 +
14274 ( -0.0000002904 )
14275 * t) * t) * t) * t) * t) * DAS2R;
14276
14277 /* Equatorial precession: minus the first of the 323 Euler angles. */
14278
14279 zetaa = ( 2.650545 +
14280 ( 2306.083227 +
14281 ( 0.2988499 +
14282 ( 0.01801828 +
14283 ( -0.000005971 +
14284 ( -0.0000003173 )
14285 * t) * t) * t) * t) * t) * DAS2R;
14286
14287 /* Equatorial precession: second of the 323 Euler angles. */
14288
14289 thetaa = ( 2004.191903 +
14290 ( -0.4294934 +
14291 ( -0.04182264 +
14292 ( -0.000007089 +
14293 ( -0.0000001274 )
14294 * t) * t) * t) * t) * t * DAS2R;
14295
14296 /* General precession. */
14297
14298 pa = ( 5028.796195 +
14299 ( 1.1054348 +
14300 ( 0.00007964 +
14301 ( -0.000023857 +
14302 ( 0.0000000383 )
14303 * t) * t) * t) * t) * t * DAS2R;
14304
14305 /* Fukushima-Williams angles for precession. */
14306
14307 gam = ( 10.556403 +
14308 ( 0.4932044 +
14309 ( -0.00031238 +
14310 ( -0.000002788 +
14311 ( 0.0000000260 )
14312 * t) * t) * t) * t) * t * DAS2R;
14313
14314 phi = eps0 + ( -46.811015 +
14315 ( 0.0511269 +
14316 ( 0.00053289 +
14317 ( -0.000000440 +
14318 ( -0.0000000176 )
14319 * t) * t) * t) * t) * t * DAS2R;
14320
14321 psi = ( 5038.481507 +
14322 ( 1.5584176 +
14323 ( -0.00018522 +
14324 ( -0.000026452 +
14325 ( -0.0000000148 )
14326 * t) * t) * t) * t) * t * DAS2R;
14327
14328 return new PrecessionAngles(eps0, psia, oma, bpa, bqa, pia, bpia, epsa, chia, za, zetaa, thetaa, pa, gam, phi, psi);
14329
14330 }
14331
14332
14333 /**
14334 * Extend a p-vector to a pv-vector by appending a zero velocity.
14335 *
14336 *<p>This function is derived from the International Astronomical Union's
14337 * SOFA (Standards Of Fundamental Astronomy) software collection.
14338 *
14339 *<p>Status: vector/matrix support function.
14340 *
14341 *<!-- Given: -->
14342 * @param p double[3] p-vector
14343 *
14344 *<!-- Returned: -->
14345 * @return pv double[2][3] <u>returned</u> pv-vector
14346 *
14347 *<p>Called:<ul>
14348 * <li>{@link #jauCp} copy p-vector
14349 * <li>{@link #jauZp} zero p-vector
14350 * </ul>
14351 *@version 2008 May 11
14352 *
14353 * @since Release 20101201
14354 *
14355 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
14356 */
14357 public static double[][] jauP2pv(double p[] )
14358 {
14359 double pv[][] = new double[3][3];
14360 jauCp(p, pv[0]);
14361 jauZp(pv[1]);
14362
14363 return pv;
14364
14365 }
14366
14367 /**
14368 * A position expressed in spherical polar coordinates.
14369 * .
14370 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 21 Nov 2011
14371 * @version $Revision$ $date$
14372 */
14373 public static class SphericalPosition {
14374 /** longitude angle (radians) */
14375 public double theta;
14376 /** latitude angle (radians) */
14377 public double phi;
14378 /** radial distance */
14379 public double r;
14380 public SphericalPosition(double theta, double phi, double r) {
14381 this.theta = theta;
14382 this.phi = phi;
14383 this.r = r;
14384 }
14385 }
14386
14387 /**
14388 * P-vector to spherical polar coordinates.
14389 *
14390 *<p>This function is derived from the International Astronomical Union's
14391 * SOFA (Standards Of Fundamental Astronomy) software collection.
14392 *
14393 *<p>Status: vector/matrix support function.
14394 *
14395 *<!-- Given: -->
14396 * @param p double[3] p-vector
14397 *
14398 *<!-- Returned: -->
14399 * @return theta double <u>returned</u> longitude angle (radians)
14400 * phi double <u>returned</u> latitude angle (radians)
14401 * r double <u>returned</u> radial distance
14402 *
14403 * <p>Notes:
14404 * <ol>
14405 *
14406 * <li> If P is null, zero theta, phi and r are returned.
14407 *
14408 * <li> At either pole, zero theta is returned.
14409 *</ol>
14410 *<p>Called:<ul>
14411 * <li>{@link #jauC2s} p-vector to spherical
14412 * <li>{@link #jauPm} modulus of p-vector
14413 * </ul>
14414 *@version 2008 May 22
14415 *
14416 * @since Release 20101201
14417 *
14418 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
14419 */
14420 public static SphericalPosition jauP2s(double p[])
14421 {
14422 SphericalCoordinate sc = jauC2s(p);
14423 double r = jauPm(p);
14424
14425 return new SphericalPosition(sc.alpha, sc.delta, r);
14426
14427 }
14428
14429
14430 /**
14431 * Position-angle from two p-vectors.
14432 *
14433 *<p>This function is derived from the International Astronomical Union's
14434 * SOFA (Standards Of Fundamental Astronomy) software collection.
14435 *
14436 *<p>Status: vector/matrix support function.
14437 *
14438 *<!-- Given: -->
14439 * @param a double[3] direction of reference point
14440 * @param b double[3] direction of point whose PA is required
14441 *
14442 * <!-- Returned (function value): -->
14443 * @return double position angle of b with respect to a (radians)
14444 *
14445 * <p>Notes:
14446 * <ol>
14447 *
14448 * <li> The result is the position angle, in radians, of direction b with
14449 * respect to direction a. It is in the range -pi to +pi. The
14450 * sense is such that if b is a small distance "north" of a the
14451 * position angle is approximately zero, and if b is a small
14452 * distance "east" of a the position angle is approximately +pi/2.
14453 *
14454 * <li> The vectors a and b need not be of unit length.
14455 *
14456 * <li> Zero is returned if the two directions are the same or if either
14457 * vector is null.
14458 *
14459 * <li> If vector a is at a pole, the result is ill-defined.
14460 *</ol>
14461 *<p>Called:<ul>
14462 * <li>{@link #jauPn} decompose p-vector into modulus and direction
14463 * <li>{@link #jauPm} modulus of p-vector
14464 * <li>{@link #jauPxp} vector product of two p-vectors
14465 * <li>{@link #jauPmp} p-vector minus p-vector
14466 * <li>{@link #jauPdp} scalar product of two p-vectors
14467 * </ul>
14468 *@version 2008 May 25
14469 *
14470 * @since Release 20101201
14471 *
14472 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
14473 */
14474 public static double jauPap(double a[] , double b[] )
14475 {
14476 double am, au[] = new double[3], bm, st, ct, xa, ya, za, eta[] = new double[3], xi[] = new double[3], a2b[] = new double[3], pa;
14477
14478
14479 /* Modulus and direction of the a vector. */
14480 NormalizedVector nv = jauPn(a );
14481 am = nv.r; au = nv.u;
14482 /* Modulus of the b vector. */
14483 bm = jauPm(b);
14484
14485 /* Deal with the case of a null vector. */
14486 if ((am == 0.0) || (bm == 0.0)) {
14487 st = 0.0;
14488 ct = 1.0;
14489 } else {
14490
14491 /* The "north" axis tangential from a (arbitrary length). */
14492 xa = a[0];
14493 ya = a[1];
14494 za = a[2];
14495 eta[0] = -xa * za;
14496 eta[1] = -ya * za;
14497 eta[2] = xa*xa + ya*ya;
14498
14499 /* The "east" axis tangential from a (same length). */
14500 xi = jauPxp(eta,au);
14501
14502 /* The vector from a to b. */
14503 a2b = jauPmp(b, a);
14504
14505 /* Resolve into components along the north and east axes. */
14506 st = jauPdp(a2b, xi);
14507 ct = jauPdp(a2b, eta);
14508
14509 /* Deal with degenerate cases. */
14510 if ((st == 0.0) && (ct == 0.0)) ct = 1.0;
14511 }
14512
14513 /* Position angle. */
14514 pa = atan2(st, ct);
14515
14516 return pa;
14517
14518 }
14519
14520
14521 /**
14522 * Position-angle from spherical coordinates.
14523 *
14524 *<p>This function is derived from the International Astronomical Union's
14525 * SOFA (Standards Of Fundamental Astronomy) software collection.
14526 *
14527 *<p>Status: vector/matrix support function.
14528 *
14529 *<!-- Given: -->
14530 * @param al double longitude of point A (e.g. RA) in radians
14531 * @param ap double latitude of point A (e.g. Dec) in radians
14532 * @param bl double longitude of point B
14533 * @param bp double latitude of point B
14534 *
14535 * <!-- Returned (function value): -->
14536 * @return double position angle of B with respect to A
14537 *
14538 * <p>Notes:
14539 * <ol>
14540 *
14541 * <li> The result is the bearing (position angle), in radians, of point
14542 * B with respect to point A. It is in the range -pi to +pi. The
14543 * sense is such that if B is a small distance "east" of point A,
14544 * the bearing is approximately +pi/2.
14545 *
14546 * <li> Zero is returned if the two points are coincident.
14547 *</ol>
14548 *@version 2008 May 22
14549 *
14550 * @since Release 20101201
14551 *
14552 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
14553 */
14554 public static double jauPas(double al, double ap, double bl, double bp)
14555 {
14556 double dl, x, y, pa;
14557
14558
14559 dl = bl - al;
14560 y = sin(dl) * cos(bp);
14561 x = sin(bp) * cos(ap) - cos(bp) * sin(ap) * cos(dl);
14562 pa = ((x != 0.0) || (y != 0.0)) ? atan2(y, x) : 0.0;
14563
14564 return pa;
14565
14566 }
14567
14568
14569 /**
14570 * This function forms three Euler angles which implement general
14571 * precession from epoch J2000.0, using the IAU 2006 model. Frame
14572 * bias (the offset between ICRS and mean J2000.0) is included.
14573 *
14574 *<p>This function is derived from the International Astronomical Union's
14575 * SOFA (Standards Of Fundamental Astronomy) software collection.
14576 *
14577 *<p>Status: support function.
14578 *
14579 *<!-- Given: -->
14580 * @param date1 double TT as a 2-part Julian Date (Note 1)
14581 * @param date2 double TT as a 2-part Julian Date (Note 1)
14582 *
14583 *<!-- Returned: -->
14584 * @return bzeta 1st rotation: radians cw around z,
14585 * 3rd rotation: radians cw around z,
14586 * 2nd rotation: radians ccw around y.
14587 *
14588 * <p>Notes:
14589 * <ol>
14590 *
14591 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
14592 * convenient way between the two arguments. For example,
14593 * JD(TT)=2450123.7 could be expressed in any of these ways,
14594 * among others:
14595 *<pre>
14596 * date1 date2
14597 *
14598 * 2450123.7 0.0 (JD method)
14599 * 2451545.0 -1421.3 (J2000 method)
14600 * 2400000.5 50123.2 (MJD method)
14601 * 2450123.5 0.2 (date & time method)
14602 *</pre>
14603 * The JD method is the most natural and convenient to use in
14604 * cases where the loss of several decimal digits of resolution
14605 * is acceptable. The J2000 method is best matched to the way
14606 * the argument is handled internally and will deliver the
14607 * optimum resolution. The MJD method and the date & time methods
14608 * are both good compromises between resolution and convenience.
14609 *
14610 * <li> The traditional accumulated precession angles zeta_A, z_A,
14611 * theta_A cannot be obtained in the usual way, namely through
14612 * polynomial expressions, because of the frame bias. The latter
14613 * means that two of the angles undergo rapid changes near this
14614 * date. They are instead the results of decomposing the
14615 * precession-bias matrix obtained by using the Fukushima-Williams
14616 * method, which does not suffer from the problem. The
14617 * decomposition returns values which can be used in the
14618 * conventional formulation and which include frame bias.
14619 *
14620 * <li> The three angles are returned in the conventional order, which
14621 * is not the same as the order of the corresponding Euler
14622 * rotations. The precession-bias matrix is
14623 * R_3(-z) x R_2(+theta) x R_3(-zeta).
14624 *
14625 * <li> Should zeta_A, z_A, theta_A angles be required that do not
14626 * contain frame bias, they are available by calling the JSOFA
14627 * function jauP06e.
14628 *</ol>
14629 *<p>Called:<ul>
14630 * <li>{@link #jauPmat06} PB matrix, IAU 2006
14631 * <li>{@link #jauRz} rotate around Z-axis
14632 * </ul>
14633 *@version 2008 May 26
14634 *
14635 * @since Release 20101201
14636 *
14637 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
14638 */
14639 public static EulerAngles jauPb06(double date1, double date2)
14640 {
14641 double r[][] = new double[3][3], r31, r32;
14642
14643
14644 /* Precession matrix via Fukushima-Williams angles. */
14645 r = jauPmat06(date1, date2);
14646
14647 /* Solve for z. */
14648 double bz = atan2(r[1][2], r[0][2]);
14649
14650 /* Remove it from the matrix. */
14651 jauRz(bz, r);
14652
14653 /* Solve for the remaining two angles. */
14654 double bzeta = atan2 (r[1][0], r[1][1]);
14655 r31 = r[2][0];
14656 r32 = r[2][1];
14657 double btheta = atan2(-dsign(sqrt(r31 * r31 + r32 * r32), r[0][2]),
14658 r[2][2]);
14659
14660 return new EulerAngles(bzeta, bz, btheta);
14661
14662 }
14663
14664
14665 /**
14666 * p-vector inner (=scalar=dot) product.
14667 *
14668 *<p>This function is derived from the International Astronomical Union's
14669 * SOFA (Standards Of Fundamental Astronomy) software collection.
14670 *
14671 *<p>Status: vector/matrix support function.
14672 *
14673 *<!-- Given: -->
14674 * @param a double[3] first p-vector
14675 * @param b double[3] second p-vector
14676 *
14677 * <!-- Returned (function value): -->
14678 * @return double a . b
14679 *
14680 *@version 2008 May 22
14681 *
14682 * @since Release 20101201
14683 *
14684 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
14685 */
14686 public static double jauPdp(double a[] , double b[] )
14687 {
14688 double w;
14689
14690
14691 w = a[0] * b[0]
14692 + a[1] * b[1]
14693 + a[2] * b[2];
14694
14695 return w;
14696
14697 }
14698
14699
14700 /**
14701 * Precession angles, IAU 2006 (Fukushima-Williams 4-angle formulation).
14702 *
14703 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 1 Feb 2010
14704 *
14705 * @since AIDA Stage 1
14706 */
14707 public static class FWPrecessionAngles{
14708 /** F-W angle gamma_bar (radians) */
14709 public double gamb;
14710 /** F-W angle phi_bar (radians) */
14711 public double phib;
14712 /** F-W angle psi_bar (radians) */
14713 public double psib;
14714 /** F-W angle epsilon_A (radians) */
14715 public double epsa;
14716 public FWPrecessionAngles(double gamb, double phib, double psib, double epsa) {
14717 this.gamb = gamb;
14718 this.phib = phib;
14719 this.psib = psib;
14720 this.epsa = epsa;
14721 }
14722 }
14723 /**
14724 * Precession angles, IAU 2006 (Fukushima-Williams 4-angle formulation).
14725 *
14726 *<p>This function is derived from the International Astronomical Union's
14727 * SOFA (Standards Of Fundamental Astronomy) software collection.
14728 *
14729 *<p>Status: canonical model.
14730 *
14731 *<!-- Given: -->
14732 * @param date1 double TT as a 2-part Julian Date (Note 1)
14733 * @param date2 double TT as a 2-part Julian Date (Note 1)
14734 *
14735 *<!-- Returned: -->
14736 * @return gamb double <u>returned</u> F-W angle gamma_bar (radians)
14737 * phib double <u>returned</u> F-W angle phi_bar (radians)
14738 * psib double <u>returned</u> F-W angle psi_bar (radians)
14739 * epsa double <u>returned</u> F-W angle epsilon_A (radians)
14740 *
14741 * <p>Notes:
14742 * <ol>
14743 *
14744 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
14745 * convenient way between the two arguments. For example,
14746 * JD(TT)=2450123.7 could be expressed in any of these ways,
14747 * among others:
14748 *<pre>
14749 * date1 date2
14750 *
14751 * 2450123.7 0.0 (JD method)
14752 * 2451545.0 -1421.3 (J2000 method)
14753 * 2400000.5 50123.2 (MJD method)
14754 * 2450123.5 0.2 (date & time method)
14755 *</pre>
14756 * The JD method is the most natural and convenient to use in
14757 * cases where the loss of several decimal digits of resolution
14758 * is acceptable. The J2000 method is best matched to the way
14759 * the argument is handled internally and will deliver the
14760 * optimum resolution. The MJD method and the date & time methods
14761 * are both good compromises between resolution and convenience.
14762 *
14763 * <li> Naming the following points:
14764 *
14765 * e = J2000.0 ecliptic pole,
14766 * p = GCRS pole,
14767 * E = mean ecliptic pole of date,
14768 * and P = mean pole of date,
14769 *
14770 * the four Fukushima-Williams angles are as follows:
14771 *
14772 * gamb = gamma_bar = epE
14773 * phib = phi_bar = pE
14774 * psib = psi_bar = pEP
14775 * epsa = epsilon_A = EP
14776 *
14777 * <li> The matrix representing the combined effects of frame bias and
14778 * precession is:
14779 *
14780 * PxB = R_1(-epsa).R_3(-psib).R_1(phib).R_3(gamb)
14781 *
14782 * <li> The matrix representing the combined effects of frame bias,
14783 * precession and nutation is simply:
14784 *
14785 * NxPxB = R_1(-epsa-dE).R_3(-psib-dP).R_1(phib).R_3(gamb)
14786 *
14787 * where dP and dE are the nutation components with respect to the
14788 * ecliptic of date.
14789 *</ol>
14790 *<p>Reference:
14791 *
14792 * Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
14793 *
14794 *<p>Called:<ul>
14795 * <li>{@link #jauObl06} mean obliquity, IAU 2006
14796 * </ul>
14797 *@version 2009 December 17
14798 *
14799 * @since Release 20101201
14800 *
14801 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
14802 */
14803 public static FWPrecessionAngles jauPfw06(double date1, double date2 )
14804 {
14805 double t;
14806
14807
14808 /* Interval between fundamental date J2000.0 and given date (JC). */
14809 t = ((date1 - DJ00) + date2) / DJC;
14810
14811 /* P03 bias+precession angles. */
14812 double gamb = ( -0.052928 +
14813 ( 10.556378 +
14814 ( 0.4932044 +
14815 ( -0.00031238 +
14816 ( -0.000002788 +
14817 ( 0.0000000260 )
14818 * t) * t) * t) * t) * t) * DAS2R;
14819 double phib = ( 84381.412819 +
14820 ( -46.811016 +
14821 ( 0.0511268 +
14822 ( 0.00053289 +
14823 ( -0.000000440 +
14824 ( -0.0000000176 )
14825 * t) * t) * t) * t) * t) * DAS2R;
14826 double psib = ( -0.041775 +
14827 ( 5038.481484 +
14828 ( 1.5584175 +
14829 ( -0.00018522 +
14830 ( -0.000026452 +
14831 ( -0.0000000148 )
14832 * t) * t) * t) * t) * t) * DAS2R;
14833 double epsa = jauObl06(date1, date2);
14834
14835 return new FWPrecessionAngles(gamb, phib, psib, epsa);
14836
14837 }
14838
14839
14840 /**
14841 *<p>This function is derived from the International Astronomical Union's
14842 * SOFA (Standards Of Fundamental Astronomy) software collection.
14843 *
14844 *<p>Status: support function.
14845 *
14846 * Approximate heliocentric position and velocity of a nominated major
14847 * planet: Mercury, Venus, EMB, Mars, Jupiter, Saturn, Uranus or
14848 * Neptune (but not the Earth itself).
14849 *
14850 *<!-- Given: -->
14851 * @param date1 double TDB date part A (Note 1)
14852 * @param date2 double TDB date part B (Note 1)
14853 * @param np int planet (1=Mercury, 2=Venus, 3=EMB, 4=Mars,
14854 * 5=Jupiter, 6=Saturn, 7=Uranus, 8=Neptune)
14855 *
14856 * Returned (argument):
14857 * @param pv double[3][2] (returned) planet p,v (heliocentric, J2000.0, AU,AU/d)
14858 *
14859 * <!-- Returned (function value): -->
14860 * @return int status: -1 = illegal NP (outside 1-8)
14861 * 0 = OK
14862 * +1 = warning: year outside 1000-3000
14863 * +2 = warning: failed to converge
14864 *
14865 * <p>Notes:
14866 * <ol>
14867 *
14868 * <li> The date date1+date2 is in the TDB time scale (in practice TT can
14869 * be used) and is a Julian Date, apportioned in any convenient way
14870 * between the two arguments. For example, JD(TDB)=2450123.7 could
14871 * be expressed in any of these ways, among others:
14872 *<pre>
14873 * date1 date2
14874 *
14875 * 2450123.7 0.0 (JD method)
14876 * 2451545.0 -1421.3 (J2000 method)
14877 * 2400000.5 50123.2 (MJD method)
14878 * 2450123.5 0.2 (date & time method)
14879 *</pre>
14880 * The JD method is the most natural and convenient to use in cases
14881 * where the loss of several decimal digits of resolution is
14882 * acceptable. The J2000 method is best matched to the way the
14883 * argument is handled internally and will deliver the optimum
14884 * resolution. The MJD method and the date & time methods are both
14885 * good compromises between resolution and convenience. The limited
14886 * accuracy of the present algorithm is such that any of the methods
14887 * is satisfactory.
14888 *
14889 * <li> If an np value outside the range 1-8 is supplied, an error status
14890 * (function value -1) is returned and the pv vector set to zeroes.
14891 *
14892 * <li> For np=3 the result is for the Earth-Moon Barycenter. To obtain
14893 * the heliocentric position and velocity of the Earth, use instead
14894 * the JSOFA function jauEpv00.
14895 *
14896 * <li> On successful return, the array pv contains the following:
14897 *<pre>
14898 * pv[0][0] x }
14899 * pv[1][0] y } heliocentric position, AU
14900 * pv[2][0] z }
14901 *
14902 * pv[0][1] xdot }
14903 * pv[1][1] ydot } heliocentric velocity, AU/d
14904 * pv[2][1] zdot }
14905 *</pre>
14906 * The reference frame is equatorial and is with respect to the
14907 * mean equator and equinox of epoch J2000.0.
14908 *
14909 * <li> The algorithm is due to J.L. Simon, P. Bretagnon, J. Chapront,
14910 * M. Chapront-Touze, G. Francou and J. Laskar (Bureau des
14911 * Longitudes, Paris, France). From comparisons with JPL
14912 * ephemeris DE102, they quote the following maximum errors
14913 * over the interval 1800-2050:
14914 *<pre>
14915 * L (arcsec) B (arcsec) R (km)
14916 *
14917 * Mercury 4 1 300
14918 * Venus 5 1 800
14919 * EMB 6 1 1000
14920 * Mars 17 1 7700
14921 * Jupiter 71 5 76000
14922 * Saturn 81 13 267000
14923 * Uranus 86 7 712000
14924 * Neptune 11 1 253000
14925 *</pre>
14926 * Over the interval 1000-3000, they report that the accuracy is no
14927 * worse than 1.5 times that over 1800-2050. Outside 1000-3000 the
14928 * accuracy declines.
14929 *
14930 * Comparisons of the present function with the JPL DE200 ephemeris
14931 * give the following RMS errors over the interval 1960-2025:
14932 *<pre>
14933 * position (km) velocity (m/s)
14934 *
14935 * Mercury 334 0.437
14936 * Venus 1060 0.855
14937 * EMB 2010 0.815
14938 * Mars 7690 1.98
14939 * Jupiter 71700 7.70
14940 * Saturn 199000 19.4
14941 * Uranus 564000 16.4
14942 * Neptune 158000 14.4
14943 *</pre>
14944 * Comparisons against DE200 over the interval 1800-2100 gave the
14945 * following maximum absolute differences. (The results using
14946 * DE406 were essentially the same.)
14947 *<pre>
14948 * L (arcsec) B (arcsec) R (km) Rdot (m/s)
14949 *
14950 * Mercury 7 1 500 0.7
14951 * Venus 7 1 1100 0.9
14952 * EMB 9 1 1300 1.0
14953 * Mars 26 1 9000 2.5
14954 * Jupiter 78 6 82000 8.2
14955 * Saturn 87 14 263000 24.6
14956 * Uranus 86 7 661000 27.4
14957 * Neptune 11 2 248000 21.4
14958 *</pre>
14959 * <li> The present JSOFA re-implementation of the original Simon et al.
14960 * Fortran code differs from the original in the following respects:
14961 *<ul>
14962 * <li> C instead of Fortran.
14963 *
14964 * <li> The date is supplied in two parts.
14965 *
14966 * <li> The result is returned only in equatorial Cartesian form;
14967 * the ecliptic longitude, latitude and radius vector are not
14968 * returned.
14969 *
14970 * <li> The result is in the J2000.0 equatorial frame, not ecliptic.
14971 *
14972 * <li> More is done in-line: there are fewer calls to subroutines.
14973 *
14974 * <li> Different error/warning status values are used.
14975 *
14976 * <li> A different Kepler's-equation-solver is used (avoiding
14977 * use of double precision complex).
14978 *
14979 * <li> Polynomials in t are nested to minimize rounding errors.
14980 *
14981 * <li> Explicit double constants are used to avoid mixed-mode
14982 * expressions.
14983 *</ul>
14984 * None of the above changes affects the result significantly.
14985 *
14986 * <li> The returned status indicates the most serious condition
14987 * encountered during execution of the function. Illegal np is
14988 * considered the most serious, overriding failure to converge,
14989 * which in turn takes precedence over the remote date warning.
14990 *</ol>
14991 *<p>Called:<ul>
14992 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
14993 * </ul>
14994 *<p>Reference: Simon, J.L, Bretagnon, P., Chapront, J.,
14995 * Chapront-Touze, M., Francou, G., and Laskar, J.,
14996 * Astron. Astrophys. 282, 663 (1994).
14997 *
14998 *@version 2009 December 17
14999 *
15000 * @since Release 20101201
15001 *
15002 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
15003 */
15004 public static int jauPlan94(double date1, double date2, int np, double pv[][])
15005 {
15006 /* Gaussian constant */
15007 final double GK = 0.017202098950;
15008
15009 /* Sin and cos of J2000.0 mean obliquity (IAU 1976) */
15010 final double SINEPS = 0.3977771559319137;
15011 final double COSEPS = 0.9174820620691818;
15012
15013 /* Maximum number of iterations allowed to solve Kepler's equation */
15014 final int KMAX = 10;
15015
15016 int jstat, i, k;
15017 double t, da, dl, de, dp, di, dom, dmu, arga, argl, am,
15018 ae, dae, ae2, at, r, v, si2, xq, xp, tl, xsw,
15019 xcw, xm2, xf, ci2, xms, xmc, xpxq2, x, y, z;
15020
15021 /* Planetary inverse masses */
15022 final double amas[] = { 6023600.0, /* Mercury */
15023 408523.5, /* Venus */
15024 328900.5, /* EMB */
15025 3098710.0, /* Mars */
15026 1047.355, /* Jupiter */
15027 3498.5, /* Saturn */
15028 22869.0, /* Uranus */
15029 19314.0 }; /* Neptune */
15030
15031 /*
15032 * Tables giving the mean Keplerian elements, limited to t^2 terms:
15033 *
15034 * a semi-major axis (AU)
15035 * dlm mean longitude (degree and arcsecond)
15036 * e eccentricity
15037 * pi longitude of the perihelion (degree and arcsecond)
15038 * dinc inclination (degree and arcsecond)
15039 * omega longitude of the ascending node (degree and arcsecond)
15040 */
15041
15042 final double a[][] = {
15043 { 0.3870983098, 0.0, 0.0 }, /* Mercury */
15044 { 0.7233298200, 0.0, 0.0 }, /* Venus */
15045 { 1.0000010178, 0.0, 0.0 }, /* EMB */
15046 { 1.5236793419, 3e-10, 0.0 }, /* Mars */
15047 { 5.2026032092, 19132e-10, -39e-10 }, /* Jupiter */
15048 { 9.5549091915, -0.0000213896, 444e-10 }, /* Saturn */
15049 { 19.2184460618, -3716e-10, 979e-10 }, /* Uranus */
15050 { 30.1103868694, -16635e-10, 686e-10 } /* Neptune */
15051 };
15052
15053 final double dlm[][] = {
15054 { 252.25090552, 5381016286.88982, -1.92789 },
15055 { 181.97980085, 2106641364.33548, 0.59381 },
15056 { 100.46645683, 1295977422.83429, -2.04411 },
15057 { 355.43299958, 689050774.93988, 0.94264 },
15058 { 34.35151874, 109256603.77991, -30.60378 },
15059 { 50.07744430, 43996098.55732, 75.61614 },
15060 { 314.05500511, 15424811.93933, -1.75083 },
15061 { 304.34866548, 7865503.20744, 0.21103 }
15062 };
15063
15064 final double e[][] = {
15065 { 0.2056317526, 0.0002040653, -28349e-10 },
15066 { 0.0067719164, -0.0004776521, 98127e-10 },
15067 { 0.0167086342, -0.0004203654, -0.0000126734 },
15068 { 0.0934006477, 0.0009048438, -80641e-10 },
15069 { 0.0484979255, 0.0016322542, -0.0000471366 },
15070 { 0.0555481426, -0.0034664062, -0.0000643639 },
15071 { 0.0463812221, -0.0002729293, 0.0000078913 },
15072 { 0.0094557470, 0.0000603263, 0.0 }
15073 };
15074
15075 final double pi[][] = {
15076 { 77.45611904, 5719.11590, -4.83016 },
15077 { 131.56370300, 175.48640, -498.48184 },
15078 { 102.93734808, 11612.35290, 53.27577 },
15079 { 336.06023395, 15980.45908, -62.32800 },
15080 { 14.33120687, 7758.75163, 259.95938 },
15081 { 93.05723748, 20395.49439, 190.25952 },
15082 { 173.00529106, 3215.56238, -34.09288 },
15083 { 48.12027554, 1050.71912, 27.39717 }
15084 };
15085
15086 final double dinc[][] = {
15087 { 7.00498625, -214.25629, 0.28977 },
15088 { 3.39466189, -30.84437, -11.67836 },
15089 { 0.0, 469.97289, -3.35053 },
15090 { 1.84972648, -293.31722, -8.11830 },
15091 { 1.30326698, -71.55890, 11.95297 },
15092 { 2.48887878, 91.85195, -17.66225 },
15093 { 0.77319689, -60.72723, 1.25759 },
15094 { 1.76995259, 8.12333, 0.08135 }
15095 };
15096
15097 final double omega[][] = {
15098 { 48.33089304, -4515.21727, -31.79892 },
15099 { 76.67992019, -10008.48154, -51.32614 },
15100 { 174.87317577, -8679.27034, 15.34191 },
15101 { 49.55809321, -10620.90088, -230.57416 },
15102 { 100.46440702, 6362.03561, 326.52178 },
15103 { 113.66550252, -9240.19942, -66.23743 },
15104 { 74.00595701, 2669.15033, 145.93964 },
15105 { 131.78405702, -221.94322, -0.78728 }
15106 };
15107
15108 /* Tables for trigonometric terms to be added to the mean elements of */
15109 /* the semi-major axes */
15110
15111 final double kp[][] = {
15112 { 69613, 75645, 88306, 59899, 15746, 71087, 142173, 3086, 0 },
15113 { 21863, 32794, 26934, 10931, 26250, 43725, 53867, 28939, 0 },
15114 { 16002, 21863, 32004, 10931, 14529, 16368, 15318, 32794, 0 },
15115 { 6345, 7818, 15636, 7077, 8184, 14163, 1107, 4872, 0 },
15116 { 1760, 1454, 1167, 880, 287, 2640, 19, 2047, 1454 },
15117 { 574, 0, 880, 287, 19, 1760, 1167, 306, 574 },
15118 { 204, 0, 177, 1265, 4, 385, 200, 208, 204 },
15119 { 0, 102, 106, 4, 98, 1367, 487, 204, 0 }
15120 };
15121
15122 final double ca[][] = {
15123 { 4, -13, 11, -9, -9, -3, -1, 4, 0 },
15124 { -156, 59, -42, 6, 19, -20, -10, -12, 0 },
15125 { 64, -152, 62, -8, 32, -41, 19, -11, 0 },
15126 { 124, 621, -145, 208, 54, -57, 30, 15, 0 },
15127 { -23437, -2634, 6601, 6259, -1507,-1821, 2620, -2115, -1489 },
15128 { 62911,-119919, 79336,17814,-24241,12068, 8306, -4893, 8902 },
15129 { 389061,-262125,-44088, 8387,-22976,-2093, -615, -9720, 6633 },
15130 { -412235,-157046,-31430,37817, -9740, -13, -7449, 9644, 0 }
15131 };
15132
15133 final double sa[][] = {
15134 { -29, -1, 9, 6, -6, 5, 4, 0, 0 },
15135 { -48, -125, -26, -37, 18, -13, -20, -2, 0 },
15136 { -150, -46, 68, 54, 14, 24, -28, 22, 0 },
15137 { -621, 532, -694, -20, 192, -94, 71, -73, 0 },
15138 { -14614,-19828, -5869, 1881, -4372, -2255, 782, 930, 913 },
15139 { 139737, 0, 24667, 51123, -5102, 7429, -4095, -1976, -9566 },
15140 { -138081, 0, 37205,-49039,-41901,-33872,-27037,-12474, 18797 },
15141 { 0, 28492,133236, 69654, 52322,-49577,-26430, -3593, 0 }
15142 };
15143
15144 /* Tables giving the trigonometric terms to be added to the mean */
15145 /* elements of the mean longitudes */
15146
15147 final double kq[][] = {
15148 { 3086,15746,69613,59899,75645,88306, 12661, 2658, 0, 0 },
15149 { 21863,32794,10931, 73, 4387,26934, 1473, 2157, 0, 0 },
15150 { 10,16002,21863,10931, 1473,32004, 4387, 73, 0, 0 },
15151 { 10, 6345, 7818, 1107,15636, 7077, 8184, 532, 10, 0 },
15152 { 19, 1760, 1454, 287, 1167, 880, 574, 2640, 19, 1454 },
15153 { 19, 574, 287, 306, 1760, 12, 31, 38, 19, 574 },
15154 { 4, 204, 177, 8, 31, 200, 1265, 102, 4, 204 },
15155 { 4, 102, 106, 8, 98, 1367, 487, 204, 4, 102 }
15156 };
15157
15158 final double cl[][] = {
15159 { 21, -95, -157, 41, -5, 42, 23, 30, 0, 0 },
15160 { -160, -313, -235, 60, -74, -76, -27, 34, 0, 0 },
15161 { -325, -322, -79, 232, -52, 97, 55, -41, 0, 0 },
15162 { 2268, -979, 802, 602, -668, -33, 345, 201, -55, 0 },
15163 { 7610, -4997,-7689,-5841,-2617, 1115,-748,-607, 6074, 354 },
15164 { -18549, 30125,20012, -730, 824, 23,1289,-352, -14767, -2062 },
15165 { -135245,-14594, 4197,-4030,-5630,-2898,2540,-306, 2939, 1986 },
15166 { 89948, 2103, 8963, 2695, 3682, 1648, 866,-154, -1963, -283 }
15167 };
15168
15169 final double sl[][] = {
15170 { -342, 136, -23, 62, 66, -52, -33, 17, 0, 0 },
15171 { 524, -149, -35, 117, 151, 122, -71, -62, 0, 0 },
15172 { -105, -137, 258, 35, -116, -88,-112, -80, 0, 0 },
15173 { 854, -205, -936, -240, 140, -341, -97, -232, 536, 0 },
15174 { -56980, 8016, 1012, 1448,-3024,-3710, 318, 503, 3767, 577 },
15175 { 138606,-13478,-4964, 1441,-1319,-1482, 427, 1236, -9167, -1918 },
15176 { 71234,-41116, 5334,-4935,-1848, 66, 434, -1748, 3780, -701 },
15177 { -47645, 11647, 2166, 3194, 679, 0,-244, -419, -2531, 48 }
15178 };
15179
15180 /*--------------------------------------------------------------------*/
15181
15182 /* Validate the planet number. */
15183 if ((np < 1) || (np > 8)) {
15184 jstat = -1;
15185
15186 /* Reset the result in case of failure. */
15187 for (k = 0; k < 2; k++) {
15188 for (i = 0; i < 3; i++) {
15189 pv[k][i] = 0.0;
15190 }
15191 }
15192
15193 } else {
15194
15195 /* Decrement the planet number to start at zero. */
15196 np--;
15197
15198 /* Time: Julian millennia since J2000.0. */
15199 t = ((date1 - DJ00) + date2) / DJM;
15200
15201 /* OK status unless remote date. */
15202 jstat = abs(t) <= 1.0 ? 0 : 1;
15203
15204 /* Compute the mean elements. */
15205 da = a[np][0] +
15206 (a[np][1] +
15207 a[np][2] * t) * t;
15208 dl = (3600.0 * dlm[np][0] +
15209 (dlm[np][1] +
15210 dlm[np][2] * t) * t) * DAS2R;
15211 de = e[np][0] +
15212 ( e[np][1] +
15213 e[np][2] * t) * t;
15214 dp = jauAnpm((3600.0 * pi[np][0] +
15215 (pi[np][1] +
15216 pi[np][2] * t) * t) * DAS2R);
15217 di = (3600.0 * dinc[np][0] +
15218 (dinc[np][1] +
15219 dinc[np][2] * t) * t) * DAS2R;
15220 dom = jauAnpm((3600.0 * omega[np][0] +
15221 (omega[np][1] +
15222 omega[np][2] * t) * t) * DAS2R);
15223
15224 /* Apply the trigonometric terms. */
15225 dmu = 0.35953620 * t;
15226 for (k = 0; k < 8; k++) {
15227 arga = kp[np][k] * dmu;
15228 argl = kq[np][k] * dmu;
15229 da += (ca[np][k] * cos(arga) +
15230 sa[np][k] * sin(arga)) * 1e-7;
15231 dl += (cl[np][k] * cos(argl) +
15232 sl[np][k] * sin(argl)) * 1e-7;
15233 }
15234 arga = kp[np][8] * dmu;
15235 da += t * (ca[np][8] * cos(arga) +
15236 sa[np][8] * sin(arga)) * 1e-7;
15237 for (k = 8; k < 10; k++) {
15238 argl = kq[np][k] * dmu;
15239 dl += t * (cl[np][k] * cos(argl) +
15240 sl[np][k] * sin(argl)) * 1e-7;
15241 }
15242 dl = fmod(dl, D2PI);
15243
15244 /* Iterative soln. of Kepler's equation to get eccentric anomaly. */
15245 am = dl - dp;
15246 ae = am + de * sin(am);
15247 k = 0;
15248 dae = 1.0;
15249 while (k < KMAX && abs(dae) > 1e-12) {
15250 dae = (am - ae + de * sin(ae)) / (1.0 - de * cos(ae));
15251 ae += dae;
15252 k++;
15253 if (k == KMAX-1) jstat = 2;
15254 }
15255
15256 /* True anomaly. */
15257 ae2 = ae / 2.0;
15258 at = 2.0 * atan2(sqrt((1.0 + de) / (1.0 - de)) * sin(ae2),
15259 cos(ae2));
15260
15261 /* Distance (AU) and speed (radians per day). */
15262 r = da * (1.0 - de * cos(ae));
15263 v = GK * sqrt((1.0 + 1.0 / amas[np]) / (da * da * da));
15264
15265 si2 = sin(di / 2.0);
15266 xq = si2 * cos(dom);
15267 xp = si2 * sin(dom);
15268 tl = at + dp;
15269 xsw = sin(tl);
15270 xcw = cos(tl);
15271 xm2 = 2.0 * (xp * xcw - xq * xsw);
15272 xf = da / sqrt(1 - de * de);
15273 ci2 = cos(di / 2.0);
15274 xms = (de * sin(dp) + xsw) * xf;
15275 xmc = (de * cos(dp) + xcw) * xf;
15276 xpxq2 = 2 * xp * xq;
15277
15278 /* Position (J2000.0 ecliptic x,y,z in AU). */
15279 x = r * (xcw - xm2 * xp);
15280 y = r * (xsw + xm2 * xq);
15281 z = r * (-xm2 * ci2);
15282
15283 /* Rotate to equatorial. */
15284 pv[0][0] = x;
15285 pv[0][1] = y * COSEPS - z * SINEPS;
15286 pv[0][2] = y * SINEPS + z * COSEPS;
15287
15288 /* Velocity (J2000.0 ecliptic xdot,ydot,zdot in AU/d). */
15289 x = v * (( -1.0 + 2.0 * xp * xp) * xms + xpxq2 * xmc);
15290 y = v * (( 1.0 - 2.0 * xq * xq) * xmc - xpxq2 * xms);
15291 z = v * (2.0 * ci2 * (xp * xms + xq * xmc));
15292
15293 /* Rotate to equatorial. */
15294 pv[1][0] = x;
15295 pv[1][1] = y * COSEPS - z * SINEPS;
15296 pv[1][2] = y * SINEPS + z * COSEPS;
15297
15298 }
15299
15300 /* Return the status. */
15301 return jstat;
15302
15303 }
15304
15305
15306 /**
15307 * Modulus of p-vector.
15308 *
15309 *<p>This function is derived from the International Astronomical Union's
15310 * SOFA (Standards Of Fundamental Astronomy) software collection.
15311 *
15312 *<p>Status: vector/matrix support function.
15313 *
15314 *<!-- Given: -->
15315 * @param p double[3] p-vector
15316 *
15317 * <!-- Returned (function value): -->
15318 * @return double modulus
15319 *
15320 *@version 2008 May 22
15321 *
15322 * @since Release 20101201
15323 *
15324 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
15325 */
15326 public static double jauPm(double p[] )
15327 {
15328 double w;
15329
15330
15331 w = sqrt( p[0] * p[0]
15332 + p[1] * p[1]
15333 + p[2] * p[2] );
15334
15335 return w;
15336
15337 }
15338
15339
15340 /**
15341 * Precession matrix (including frame bias) from GCRS to a specified
15342 * date, IAU 2000 model.
15343 *
15344 *<p>This function is derived from the International Astronomical Union's
15345 * SOFA (Standards Of Fundamental Astronomy) software collection.
15346 *
15347 *<p>Status: support function.
15348 *
15349 *<!-- Given: -->
15350 * @param date1 double TT as a 2-part Julian Date (Note 1)
15351 * @param date2 double TT as a 2-part Julian Date (Note 1)
15352 *
15353 *<!-- Returned: -->
15354 * @return rbp double[3][3] <u>returned</u> bias-precession matrix (Note 2)
15355 *
15356 * <p>Notes:
15357 * <ol>
15358 *
15359 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
15360 * convenient way between the two arguments. For example,
15361 * JD(TT)=2450123.7 could be expressed in any of these ways,
15362 * among others:
15363 *<pre>
15364 * date1 date2
15365 *
15366 * 2450123.7 0.0 (JD method)
15367 * 2451545.0 -1421.3 (J2000 method)
15368 * 2400000.5 50123.2 (MJD method)
15369 * 2450123.5 0.2 (date & time method)
15370 *</pre>
15371 * The JD method is the most natural and convenient to use in
15372 * cases where the loss of several decimal digits of resolution
15373 * is acceptable. The J2000 method is best matched to the way
15374 * the argument is handled internally and will deliver the
15375 * optimum resolution. The MJD method and the date & time methods
15376 * are both good compromises between resolution and convenience.
15377 *
15378 * <li> The matrix operates in the sense V(date) = rbp * V(GCRS), where
15379 * the p-vector V(GCRS) is with respect to the Geocentric Celestial
15380 * Reference System (IAU, 2000) and the p-vector V(date) is with
15381 * respect to the mean equatorial triad of the given date.
15382 *</ol>
15383 *<p>Called:<ul>
15384 * <li>{@link #jauBp00} frame bias and precession matrices, IAU 2000
15385 * </ul>
15386 *<p>Reference:
15387 *
15388 * IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc.
15389 * 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6.
15390 * (2000)
15391 *
15392 *@version 2009 December 21
15393 *
15394 * @since Release 20101201
15395 *
15396 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
15397 */
15398 public static double[][] jauPmat00(double date1, double date2)
15399 {
15400 double rb[][] = new double[3][3], rp[][] = new double[3][3],
15401 rbp[][] = new double[3][3];
15402 /* Obtain the required matrix (discarding others). */
15403 jauBp00(date1, date2, rb, rp, rbp);
15404
15405 return rbp;
15406
15407 }
15408
15409
15410 /**
15411 * Precession matrix (including frame bias) from GCRS to a specified
15412 * date, IAU 2006 model.
15413 *
15414 *<p>This function is derived from the International Astronomical Union's
15415 * SOFA (Standards Of Fundamental Astronomy) software collection.
15416 *
15417 *<p>Status: support function.
15418 *
15419 *<!-- Given: -->
15420 * @param date1 double TT as a 2-part Julian Date (Note 1)
15421 * @param date2 double TT as a 2-part Julian Date (Note 1)
15422 *
15423 *<!-- Returned: -->
15424 * @return rbp double[3][3] <u>returned</u> bias-precession matrix (Note 2)
15425 *
15426 * <p>Notes:
15427 * <ol>
15428 *
15429 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
15430 * convenient way between the two arguments. For example,
15431 * JD(TT)=2450123.7 could be expressed in any of these ways,
15432 * among others:
15433 *<pre>
15434 * date1 date2
15435 *
15436 * 2450123.7 0.0 (JD method)
15437 * 2451545.0 -1421.3 (J2000 method)
15438 * 2400000.5 50123.2 (MJD method)
15439 * 2450123.5 0.2 (date & time method)
15440 *</pre>
15441 * The JD method is the most natural and convenient to use in
15442 * cases where the loss of several decimal digits of resolution
15443 * is acceptable. The J2000 method is best matched to the way
15444 * the argument is handled internally and will deliver the
15445 * optimum resolution. The MJD method and the date & time methods
15446 * are both good compromises between resolution and convenience.
15447 *
15448 * <li> The matrix operates in the sense V(date) = rbp * V(GCRS), where
15449 * the p-vector V(GCRS) is with respect to the Geocentric Celestial
15450 * Reference System (IAU, 2000) and the p-vector V(date) is with
15451 * respect to the mean equatorial triad of the given date.
15452 *</ol>
15453 *<p>Called:<ul>
15454 * <li>{@link #jauPfw06} bias-precession F-W angles, IAU 2006
15455 * <li>{@link #jauFw2m} F-W angles to r-matrix
15456 * </ul>
15457 *<p>References:
15458 *
15459 * <p>Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
15460 *
15461 * <p>Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
15462 *
15463 *@version 2009 December 21
15464 *
15465 * @since Release 20101201
15466 *
15467 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
15468 */
15469 public static double[][] jauPmat06(double date1, double date2)
15470 {
15471
15472 /* Bias-precession Fukushima-Williams angles. */
15473 FWPrecessionAngles fw = jauPfw06(date1, date2);
15474
15475 /* Form the matrix. */
15476 double[][] rbp = jauFw2m(fw.gamb, fw.phib, fw.psib, fw.epsa );
15477
15478 return rbp;
15479
15480 }
15481
15482
15483 /**
15484 * Precession matrix from J2000.0 to a specified date, IAU 1976 model.
15485 *
15486 *<p>This function is derived from the International Astronomical Union's
15487 * SOFA (Standards Of Fundamental Astronomy) software collection.
15488 *
15489 *<p>Status: support function.
15490 *
15491 *<!-- Given: -->
15492 * @param date1 double ending date, TT (Note 1)
15493 * @param date2 double ending date, TT (Note 1)
15494 *
15495 *<!-- Returned: -->
15496 * @return rmatp double[3][3] <u>returned</u> precession matrix, J2000.0 -> date1+date2
15497 *
15498 * <p>Notes:
15499 * <ol>
15500 *
15501 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
15502 * convenient way between the two arguments. For example,
15503 * JD(TT)=2450123.7 could be expressed in any of these ways,
15504 * among others:
15505 *<pre>
15506 * date1 date2
15507 *
15508 * 2450123.7 0.0 (JD method)
15509 * 2451545.0 -1421.3 (J2000 method)
15510 * 2400000.5 50123.2 (MJD method)
15511 * 2450123.5 0.2 (date & time method)
15512 *</pre>
15513 * The JD method is the most natural and convenient to use in
15514 * cases where the loss of several decimal digits of resolution
15515 * is acceptable. The J2000 method is best matched to the way
15516 * the argument is handled internally and will deliver the
15517 * optimum resolution. The MJD method and the date & time methods
15518 * are both good compromises between resolution and convenience.
15519 *
15520 * <li> The matrix operates in the sense V(date) = RMATP * V(J2000),
15521 * where the p-vector V(J2000) is with respect to the mean
15522 * equatorial triad of epoch J2000.0 and the p-vector V(date)
15523 * is with respect to the mean equatorial triad of the given
15524 * date.
15525 *
15526 * <li> Though the matrix method itself is rigorous, the precession
15527 * angles are expressed through canonical polynomials which are
15528 * valid only for a limited time span. In addition, the IAU 1976
15529 * precession rate is known to be imperfect. The absolute accuracy
15530 * of the present formulation is better than 0.1 arcsec from
15531 * 1960AD to 2040AD, better than 1 arcsec from 1640AD to 2360AD,
15532 * and remains below 3 arcsec for the whole of the period
15533 * 500BC to 3000AD. The errors exceed 10 arcsec outside the
15534 * range 1200BC to 3900AD, exceed 100 arcsec outside 4200BC to
15535 * 5600AD and exceed 1000 arcsec outside 6800BC to 8200AD.
15536 *</ol>
15537 *<p>Called:<ul>
15538 * <li>{@link #jauPrec76} accumulated precession angles, IAU 1976
15539 * <li>{@link #jauIr} initialize r-matrix to identity
15540 * <li>{@link #jauRz} rotate around Z-axis
15541 * <li>{@link #jauRy} rotate around Y-axis
15542 * <li>{@link #jauCr} copy r-matrix
15543 * </ul>
15544 *<p>References:
15545 *
15546 * <p>Lieske, J.H., 1979, Astron.Astrophys. 73, 282.
15547 * equations (6) & (7), p283.
15548 *
15549 * Kaplan,G.H., 1981. USNO circular no. 163, pA2.
15550 *
15551 *@version 2009 December 18
15552 *
15553 * @since Release 20101201
15554 *
15555 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
15556 */
15557 public static double[][] jauPmat76(double date1, double date2)
15558 {
15559 double wmat[][] = new double[3][3];
15560 double rmatp[][] = new double[3][3];
15561
15562 /* Precession Euler angles, J2000.0 to specified date. */
15563 EulerAngles euler = jauPrec76(DJ00, 0.0, date1, date2);
15564
15565 /* Form the rotation matrix. */
15566 jauIr( wmat);
15567 jauRz( -euler.zeta, wmat);
15568 jauRy( euler.theta, wmat);
15569 jauRz( -euler.z, wmat);
15570 jauCr(wmat, rmatp);
15571
15572 return rmatp;
15573
15574 }
15575
15576
15577 /**
15578 * P-vector subtraction.
15579 *
15580 *<p>This function is derived from the International Astronomical Union's
15581 * SOFA (Standards Of Fundamental Astronomy) software collection.
15582 *
15583 *<p>Status: vector/matrix support function.
15584 *
15585 *<!-- Given: -->
15586 * @param a double[3] first p-vector
15587 * @param b double[3] second p-vector
15588 *
15589 *<!-- Returned: -->
15590 * @return amb double[3] <u>returned</u> a - b
15591 *
15592 * Note:
15593 * It is permissible to re-use the same array for any of the
15594 * arguments.
15595 *
15596 *@version 2008 November 18
15597 *
15598 * @since Release 20101201
15599 *
15600 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
15601 */
15602 public static double[] jauPmp(double a[] , double b[] )
15603 {
15604 double amb[] = new double[3];
15605 amb[0] = a[0] - b[0];
15606 amb[1] = a[1] - b[1];
15607 amb[2] = a[2] - b[2];
15608
15609 return amb;
15610
15611 }
15612
15613 /**
15614 * A normalized vector with r being the modulus and u[3] being the unit vector.
15615 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 1 Feb 2010
15616 *
15617 * @since AIDA Stage 1
15618 */
15619 public static class NormalizedVector {
15620 public double r;
15621 public double u[];
15622 public NormalizedVector(double r, double u[] ) {
15623 this.r = r;
15624 this.u = u;
15625 }
15626 }
15627 /**
15628 * Convert a p-vector into modulus and unit vector.
15629 *
15630 *<p>This function is derived from the International Astronomical Union's
15631 * SOFA (Standards Of Fundamental Astronomy) software collection.
15632 *
15633 *<p>Status: vector/matrix support function.
15634 *
15635 *<!-- Given: -->
15636 * @param p double[3] p-vector
15637 *
15638 *<!-- Returned: -->
15639 * @return r double <u>returned</u> modulus
15640 * u double[3] <u>returned</u> unit vector
15641 *
15642 * <p>Notes:
15643 * <ol>
15644 *
15645 * <li> If p is null, the result is null. Otherwise the result is a unit
15646 * vector.
15647 *
15648 * <li> It is permissible to re-use the same array for any of the
15649 * arguments.
15650 *</ol>
15651 *<p>Called:<ul>
15652 * <li>{@link #jauPm} modulus of p-vector
15653 * <li>{@link #jauZp} zero p-vector
15654 * <li>{@link #jauSxp} multiply p-vector by scalar
15655 * </ul>
15656 *@version 2008 November 18
15657 *
15658 * @since Release 20101201
15659 *
15660 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
15661 */
15662 public static NormalizedVector jauPn(double p[])
15663 {
15664 double w;
15665
15666 /* Obtain the modulus and test for zero. */
15667 w = jauPm(p);
15668 NormalizedVector nv = new NormalizedVector(w, new double[3]);
15669 if (w == 0.0) {
15670
15671 /* Null vector. */
15672 jauZp(nv.u);
15673
15674 } else {
15675
15676 /* Unit vector. */
15677 nv.u = jauSxp(1.0/w, p);
15678 }
15679
15680
15681 return nv;
15682
15683 }
15684
15685
15686 /**
15687 * Precession-nutation, IAU 2000 model: a multi-purpose function,
15688 * supporting classical (equinox-based) use directly and CIO-based
15689 * use indirectly.
15690 *
15691 *<p>This function is derived from the International Astronomical Union's
15692 * SOFA (Standards Of Fundamental Astronomy) software collection.
15693 *
15694 *<p>Status: support function.
15695 *
15696 *<!-- Given: -->
15697 * @param date1 double TT as a 2-part Julian Date (Note 1)
15698 * @param date2 double TT as a 2-part Julian Date (Note 1)
15699 * @param dpsi double nutation (Note 2)
15700 * @param deps double nutation (Note 2)
15701 *
15702 *<!-- Returned: -->
15703 * @return epsa double <u>returned</u> mean obliquity (Note 3),
15704 * rb double[3][3] <u>returned</u> frame bias matrix (Note 4),
15705 * rp double[3][3] <u>returned</u> precession matrix (Note 5),
15706 * rbp double[3][3] <u>returned</u> bias-precession matrix (Note 6),
15707 * rn double[3][3] <u>returned</u> nutation matrix (Note 7),
15708 * rbpn double[3][3] <u>returned</u> GCRS-to-true matrix (Note 8)
15709 *
15710 * <p>Notes:
15711 * <ol>
15712 *
15713 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
15714 * convenient way between the two arguments. For example,
15715 * JD(TT)=2450123.7 could be expressed in any of these ways,
15716 * among others:
15717 *<pre>
15718 * date1 date2
15719 *
15720 * 2450123.7 0.0 (JD method)
15721 * 2451545.0 -1421.3 (J2000 method)
15722 * 2400000.5 50123.2 (MJD method)
15723 * 2450123.5 0.2 (date & time method)
15724 *</pre>
15725 * The JD method is the most natural and convenient to use in
15726 * cases where the loss of several decimal digits of resolution
15727 * is acceptable. The J2000 method is best matched to the way
15728 * the argument is handled internally and will deliver the
15729 * optimum resolution. The MJD method and the date & time methods
15730 * are both good compromises between resolution and convenience.
15731 *
15732 * <li> The caller is responsible for providing the nutation components;
15733 * they are in longitude and obliquity, in radians and are with
15734 * respect to the equinox and ecliptic of date. For high-accuracy
15735 * applications, free core nutation should be included as well as
15736 * any other relevant corrections to the position of the CIP.
15737 *
15738 * <li> The returned mean obliquity is consistent with the IAU 2000
15739 * precession-nutation models.
15740 *
15741 * <li> The matrix rb transforms vectors from GCRS to J2000.0 mean
15742 * equator and equinox by applying frame bias.
15743 *
15744 * <li> The matrix rp transforms vectors from J2000.0 mean equator and
15745 * equinox to mean equator and equinox of date by applying
15746 * precession.
15747 *
15748 * <li> The matrix rbp transforms vectors from GCRS to mean equator and
15749 * equinox of date by applying frame bias then precession. It is
15750 * the product rp x rb.
15751 *
15752 * <li> The matrix rn transforms vectors from mean equator and equinox of
15753 * date to true equator and equinox of date by applying the nutation
15754 * (luni-solar + planetary).
15755 *
15756 * <li> The matrix rbpn transforms vectors from GCRS to true equator and
15757 * equinox of date. It is the product rn x rbp, applying frame
15758 * bias, precession and nutation in that order.
15759 *
15760 * <li> It is permissible to re-use the same array in the returned
15761 * arguments. The arrays are filled in the order given.
15762 *</ol>
15763 *<p>Called:<ul>
15764 * <li>{@link #jauPr00} IAU 2000 precession adjustments
15765 * <li>{@link #jauObl80} mean obliquity, IAU 1980
15766 * <li>{@link #jauBp00} frame bias and precession matrices, IAU 2000
15767 * <li>{@link #jauCr} copy r-matrix
15768 * <li>{@link #jauNumat} form nutation matrix
15769 * <li>{@link #jauRxr} product of two r-matrices
15770 * </ul>
15771 *<p>Reference:
15772 *
15773 * <p>Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
15774 * "Expressions for the Celestial Intermediate Pole and Celestial
15775 * Ephemeris Origin consistent with the IAU 2000A precession-
15776 * nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
15777 *
15778 * n.b. The celestial ephemeris origin (CEO) was renamed "celestial
15779 * intermediate origin" (CIO) by IAU 2006 Resolution 2.
15780 *
15781 *@version 2010 January 18
15782 *
15783 * @since Release 20101201
15784 *
15785 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
15786 */
15787 public static PrecessionNutation jauPn00(double date1, double date2, double dpsi, double deps)
15788 {
15789 double rbpw[][] = new double[3][3], rnw[][] = new double[3][3];
15790 double[][] rb = new double[3][3];
15791 double[][] rp = new double[3][3];
15792 double[][] rbp = new double[3][3];
15793 double[][] rn = new double[3][3];
15794 double[][] rbpn = new double[3][3];
15795
15796
15797 /* IAU 2000 precession-rate adjustments. */
15798 PrecessionDeltaTerms nut = jauPr00(date1, date2);
15799
15800 /* Mean obliquity, consistent with IAU 2000 precession-nutation. */
15801 double epsa = jauObl80(date1, date2) + nut.depspr;
15802
15803 /* Frame bias and precession matrices and their product. */
15804 jauBp00(date1, date2, rb, rp, rbpw);
15805 jauCr(rbpw, rbp);
15806
15807 /* Nutation matrix. */
15808 rnw = jauNumat(epsa, dpsi, deps);
15809 jauCr(rnw, rn);
15810
15811 /* Bias-precession-nutation matrix (classical). */
15812 rbpn = jauRxr(rnw, rbpw);
15813
15814 return new PrecessionNutation(dpsi, deps, epsa, rb, rp, rbp, rn, rbpn);
15815
15816 }
15817
15818
15819 /**
15820 * Precession-nutation model.
15821 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 4 Feb 2010
15822 *
15823 * @since AIDA Stage 1
15824 */
15825 public static class PrecessionNutation {
15826 public NutationTerms nut;
15827 /** mean obliquity */
15828 public double epsa;
15829 /** frame bias matrix */
15830 public double rb[][];
15831 /** precession matrix */
15832 public double rp[][];
15833 /** bias-precession matrix */
15834 public double rbp[][];
15835 /** nutation matrix */
15836 public double rn[][];
15837 /** GCRS-to-true matrix */
15838 public double rbpn[][];
15839 public PrecessionNutation(double dpsi, double deps, double epsa,
15840 double rb[][], double rp[][], double rbp[][],
15841 double rn[][], double rbpn[][]){
15842 this.nut = new NutationTerms(dpsi, deps);
15843 this.epsa = epsa;
15844 this.rb = rb;
15845 this.rp = rp;
15846 this.rbp = rbp;
15847 this.rn = rn;
15848 this.rbpn = rbpn;
15849 }
15850
15851 }
15852 /**
15853 * Precession-nutation, IAU 2000A model: a multi-purpose function,
15854 * supporting classical (equinox-based) use directly and CIO-based
15855 * use indirectly.
15856 *
15857 *<p>This function is derived from the International Astronomical Union's
15858 * SOFA (Standards Of Fundamental Astronomy) software collection.
15859 *
15860 *<p>Status: support function.
15861 *
15862 *<!-- Given: -->
15863 * @param date1 double TT as a 2-part Julian Date (Note 1)
15864 * @param date2 double TT as a 2-part Julian Date (Note 1)
15865 *
15866 *<!-- Returned: -->
15867 * @return dpsi double <u>returned</u> nutation (Note 2)
15868 * deps double <u>returned</u> nutation (Note 2)
15869 * epsa double <u>returned</u> mean obliquity (Note 3)
15870 * rb double[3][3] <u>returned</u> frame bias matrix (Note 4)
15871 * rp double[3][3] <u>returned</u> precession matrix (Note 5)
15872 * rbp double[3][3] <u>returned</u> bias-precession matrix (Note 6)
15873 * rn double[3][3] <u>returned</u> nutation matrix (Note 7)
15874 * rbpn double[3][3] <u>returned</u> GCRS-to-true matrix (Notes 8,9)
15875 *
15876 * <p>Notes:
15877 * <ol>
15878 *
15879 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
15880 * convenient way between the two arguments. For example,
15881 * JD(TT)=2450123.7 could be expressed in any of these ways,
15882 * among others:
15883 *<pre>
15884 * date1 date2
15885 *
15886 * 2450123.7 0.0 (JD method)
15887 * 2451545.0 -1421.3 (J2000 method)
15888 * 2400000.5 50123.2 (MJD method)
15889 * 2450123.5 0.2 (date & time method)
15890 *</pre>
15891 * The JD method is the most natural and convenient to use in
15892 * cases where the loss of several decimal digits of resolution
15893 * is acceptable. The J2000 method is best matched to the way
15894 * the argument is handled internally and will deliver the
15895 * optimum resolution. The MJD method and the date & time methods
15896 * are both good compromises between resolution and convenience.
15897 *
15898 * <li> The nutation components (luni-solar + planetary, IAU 2000A) in
15899 * longitude and obliquity are in radians and with respect to the
15900 * equinox and ecliptic of date. Free core nutation is omitted;
15901 * for the utmost accuracy, use the jauPn00 function, where the
15902 * nutation components are caller-specified. For faster but
15903 * slightly less accurate results, use the jauPn00b function.
15904 *
15905 * <li> The mean obliquity is consistent with the IAU 2000 precession.
15906 *
15907 * <li> The matrix rb transforms vectors from GCRS to J2000.0 mean
15908 * equator and equinox by applying frame bias.
15909 *
15910 * <li> The matrix rp transforms vectors from J2000.0 mean equator and
15911 * equinox to mean equator and equinox of date by applying
15912 * precession.
15913 *
15914 * <li> The matrix rbp transforms vectors from GCRS to mean equator and
15915 * equinox of date by applying frame bias then precession. It is
15916 * the product rp x rb.
15917 *
15918 * <li> The matrix rn transforms vectors from mean equator and equinox
15919 * of date to true equator and equinox of date by applying the
15920 * nutation (luni-solar + planetary).
15921 *
15922 * <li> The matrix rbpn transforms vectors from GCRS to true equator and
15923 * equinox of date. It is the product rn x rbp, applying frame
15924 * bias, precession and nutation in that order.
15925 *
15926 * <li> The X,Y,Z coordinates of the IAU 2000A Celestial Intermediate
15927 * Pole are elements (3,1-3) of the GCRS-to-true matrix,
15928 * i.e. rbpn[2][0-2].
15929 *
15930 * <li> It is permissible to re-use the same array in the returned
15931 * arguments. The arrays are filled in the order given.
15932 *</ol>
15933 *<p>Called:<ul>
15934 * <li>{@link #jauNut00a} nutation, IAU 2000A
15935 * <li>{@link #jauPn00} bias/precession/nutation results, IAU 2000
15936 * </ul>
15937 *<p>Reference:
15938 *
15939 * <p>Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
15940 * "Expressions for the Celestial Intermediate Pole and Celestial
15941 * Ephemeris Origin consistent with the IAU 2000A precession-
15942 * nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
15943 *
15944 * n.b. The celestial ephemeris origin (CEO) was renamed "celestial
15945 * intermediate origin" (CIO) by IAU 2006 Resolution 2.
15946 *
15947 *@version 2010 January 18
15948 *
15949 * @since Release 20101201
15950 *
15951 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
15952 */
15953 public static PrecessionNutation jauPn00a(double date1, double date2)
15954 {
15955 /* Nutation. */
15956 NutationTerms nut = jauNut00a(date1, date2);
15957
15958 /* Remaining results. */
15959 return jauPn00(date1, date2, nut.dpsi, nut.deps);
15960
15961
15962 }
15963
15964
15965 /**
15966 * Precession-nutation, IAU 2000B model: a multi-purpose function,
15967 * supporting classical (equinox-based) use directly and CIO-based
15968 * use indirectly.
15969 *
15970 *<p>This function is derived from the International Astronomical Union's
15971 * SOFA (Standards Of Fundamental Astronomy) software collection.
15972 *
15973 *<p>Status: support function.
15974 *
15975 *<!-- Given: -->
15976 * @param date1 double TT as a 2-part Julian Date (Note 1)
15977 * @param date2 double TT as a 2-part Julian Date (Note 1)
15978 *
15979 *<!-- Returned: -->
15980 * @return dpsi,deps double <u>returned</u> nutation (Note 2)
15981 * epsa double <u>returned</u> mean obliquity (Note 3)
15982 * rb double[3][3] <u>returned</u> frame bias matrix (Note 4)
15983 * rp double[3][3] <u>returned</u> precession matrix (Note 5)
15984 * rbp double[3][3] <u>returned</u> bias-precession matrix (Note 6)
15985 * rn double[3][3] <u>returned</u> nutation matrix (Note 7)
15986 * rbpn double[3][3] <u>returned</u> GCRS-to-true matrix (Notes 8,9)
15987 *
15988 * <p>Notes:
15989 * <ol>
15990 *
15991 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
15992 * convenient way between the two arguments. For example,
15993 * JD(TT)=2450123.7 could be expressed in any of these ways,
15994 * among others:
15995 *<pre>
15996 * date1 date2
15997 *
15998 * 2450123.7 0.0 (JD method)
15999 * 2451545.0 -1421.3 (J2000 method)
16000 * 2400000.5 50123.2 (MJD method)
16001 * 2450123.5 0.2 (date & time method)
16002 *</pre>
16003 * The JD method is the most natural and convenient to use in
16004 * cases where the loss of several decimal digits of resolution
16005 * is acceptable. The J2000 method is best matched to the way
16006 * the argument is handled internally and will deliver the
16007 * optimum resolution. The MJD method and the date & time methods
16008 * are both good compromises between resolution and convenience.
16009 *
16010 * <li> The nutation components (luni-solar + planetary, IAU 2000B) in
16011 * longitude and obliquity are in radians and with respect to the
16012 * equinox and ecliptic of date. For more accurate results, but
16013 * at the cost of increased computation, use the jauPn00a function.
16014 * For the utmost accuracy, use the jauPn00 function, where the
16015 * nutation components are caller-specified.
16016 *
16017 * <li> The mean obliquity is consistent with the IAU 2000 precession.
16018 *
16019 * <li> The matrix rb transforms vectors from GCRS to J2000.0 mean
16020 * equator and equinox by applying frame bias.
16021 *
16022 * <li> The matrix rp transforms vectors from J2000.0 mean equator and
16023 * equinox to mean equator and equinox of date by applying
16024 * precession.
16025 *
16026 * <li> The matrix rbp transforms vectors from GCRS to mean equator and
16027 * equinox of date by applying frame bias then precession. It is
16028 * the product rp x rb.
16029 *
16030 * <li> The matrix rn transforms vectors from mean equator and equinox
16031 * of date to true equator and equinox of date by applying the
16032 * nutation (luni-solar + planetary).
16033 *
16034 * <li> The matrix rbpn transforms vectors from GCRS to true equator and
16035 * equinox of date. It is the product rn x rbp, applying frame
16036 * bias, precession and nutation in that order.
16037 *
16038 * <li> The X,Y,Z coordinates of the IAU 2000B Celestial Intermediate
16039 * Pole are elements (3,1-3) of the matrix rbpn.
16040 *
16041 * <li> It is permissible to re-use the same array in the returned
16042 * arguments. The arrays are filled in the stated order.
16043 *</ol>
16044 *<p>Called:<ul>
16045 * <li>{@link #jauNut00b} nutation, IAU 2000B
16046 * <li>{@link #jauPn00} bias/precession/nutation results, IAU 2000
16047 * </ul>
16048 *<p>Reference:
16049 *
16050 * <p>Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
16051 * "Expressions for the Celestial Intermediate Pole and Celestial
16052 * Ephemeris Origin consistent with the IAU 2000A precession-
16053 * nutation model", Astron.Astrophys. 400, 1145-1154 (2003).
16054 *
16055 * n.b. The celestial ephemeris origin (CEO) was renamed "celestial
16056 * intermediate origin" (CIO) by IAU 2006 Resolution 2.
16057 *
16058 *@version 2010 January 18
16059 *
16060 * @since Release 20101201
16061 *
16062 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16063 */
16064 public static PrecessionNutation jauPn00b(double date1, double date2)
16065 {
16066 /* Nutation. */
16067 NutationTerms nut = jauNut00b(date1, date2);
16068
16069 /* Remaining results. */
16070 return jauPn00(date1, date2, nut.dpsi, nut.deps);
16071
16072
16073 }
16074
16075
16076 /**
16077 * Precession-nutation, IAU 2006 model: a multi-purpose function,
16078 * supporting classical (equinox-based) use directly and CIO-based use
16079 * indirectly.
16080 *
16081 *<p>This function is derived from the International Astronomical Union's
16082 * SOFA (Standards Of Fundamental Astronomy) software collection.
16083 *
16084 *<p>Status: support function.
16085 *
16086 *<!-- Given: -->
16087 * @param date1 double TT as a 2-part Julian Date (Note 1)
16088 * @param date2 double TT as a 2-part Julian Date (Note 1)
16089 * @param dpsi double nutation (Note 2)
16090 * @param deps double nutation (Note 2)
16091 *
16092 *<!-- Returned: -->
16093 * @return epsa double <u>returned</u> mean obliquity (Note 3)
16094 * rb double[3][3] <u>returned</u> frame bias matrix (Note 4)
16095 * rp double[3][3] <u>returned</u> precession matrix (Note 5)
16096 * rbp double[3][3] <u>returned</u> bias-precession matrix (Note 6)
16097 * rn double[3][3] <u>returned</u> nutation matrix (Note 7)
16098 * rbpn double[3][3] <u>returned</u> GCRS-to-true matrix (Note 8)
16099 *
16100 * <p>Notes:
16101 * <ol>
16102 *
16103 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
16104 * convenient way between the two arguments. For example,
16105 * JD(TT)=2450123.7 could be expressed in any of these ways,
16106 * among others:
16107 *<pre>
16108 * date1 date2
16109 *
16110 * 2450123.7 0.0 (JD method)
16111 * 2451545.0 -1421.3 (J2000 method)
16112 * 2400000.5 50123.2 (MJD method)
16113 * 2450123.5 0.2 (date & time method)
16114 *</pre>
16115 * The JD method is the most natural and convenient to use in
16116 * cases where the loss of several decimal digits of resolution
16117 * is acceptable. The J2000 method is best matched to the way
16118 * the argument is handled internally and will deliver the
16119 * optimum resolution. The MJD method and the date & time methods
16120 * are both good compromises between resolution and convenience.
16121 *
16122 * <li> The caller is responsible for providing the nutation components;
16123 * they are in longitude and obliquity, in radians and are with
16124 * respect to the equinox and ecliptic of date. For high-accuracy
16125 * applications, free core nutation should be included as well as
16126 * any other relevant corrections to the position of the CIP.
16127 *
16128 * <li> The returned mean obliquity is consistent with the IAU 2006
16129 * precession.
16130 *
16131 * <li> The matrix rb transforms vectors from GCRS to J2000.0 mean
16132 * equator and equinox by applying frame bias.
16133 *
16134 * <li> The matrix rp transforms vectors from J2000.0 mean equator and
16135 * equinox to mean equator and equinox of date by applying
16136 * precession.
16137 *
16138 * <li> The matrix rbp transforms vectors from GCRS to mean equator and
16139 * equinox of date by applying frame bias then precession. It is
16140 * the product rp x rb.
16141 *
16142 * <li> The matrix rn transforms vectors from mean equator and equinox
16143 * of date to true equator and equinox of date by applying the
16144 * nutation (luni-solar + planetary).
16145 *
16146 * <li> The matrix rbpn transforms vectors from GCRS to true equator and
16147 * equinox of date. It is the product rn x rbp, applying frame
16148 * bias, precession and nutation in that order.
16149 *
16150 * <li> The X,Y,Z coordinates of the IAU 2000B Celestial Intermediate
16151 * Pole are elements (3,1-3) of the matrix rbpn.
16152 *
16153 * <li> It is permissible to re-use the same array in the returned
16154 * arguments. The arrays are filled in the stated order.
16155 *</ol>
16156 *<p>Called:<ul>
16157 * <li>{@link #jauPfw06} bias-precession F-W angles, IAU 2006
16158 * <li>{@link #jauFw2m} F-W angles to r-matrix
16159 * <li>{@link #jauCr} copy r-matrix
16160 * <li>{@link #jauTr} transpose r-matrix
16161 * <li>{@link #jauRxr} product of two r-matrices
16162 * </ul>
16163 *<p>References:
16164 *
16165 * <p>Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
16166 *
16167 * <p>Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
16168 *
16169 *@version 2009 December 17
16170 *
16171 * @since Release 20101201
16172 *
16173 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16174 */
16175 public static PrecessionNutation jauPn06(double date1, double date2, double dpsi, double deps)
16176 {
16177
16178 double rb[][] = new double[3][3], rbp[][] = new double[3][3], rbpn[][] = new double[3][3];
16179 /* Bias-precession Fukushima-Williams angles of J2000.0 = frame bias. */
16180 FWPrecessionAngles fw = jauPfw06(DJM0, DJM00);
16181
16182 /* B matrix. */
16183 double[][] r1 = jauFw2m(fw.gamb, fw.phib, fw.psib, fw.epsa);
16184 jauCr(r1, rb);
16185
16186 /* Bias-precession Fukushima-Williams angles of date. */
16187 fw = jauPfw06(date1, date2);
16188
16189 /* Bias-precession matrix. */
16190 double[][] r2 = jauFw2m(fw.gamb, fw.phib, fw.psib, fw.epsa );
16191 jauCr(r2, rbp);
16192
16193 /* Solve for precession matrix. */
16194 double[][] rt = jauTr(r1);
16195 double[][] rp = jauRxr(r2, rt);
16196
16197 /* Equinox-based bias-precession-nutation matrix. */
16198 r1 = jauFw2m(fw.gamb, fw.phib, fw.psib + dpsi, fw.epsa + deps);
16199 jauCr(r1, rbpn);
16200
16201 /* Solve for nutation matrix. */
16202 rt = jauTr(r2);
16203 double[][] rn = jauRxr(r1, rt);
16204
16205 /* Obliquity, mean of date. */
16206 double epsa = fw.epsa;
16207
16208 return new PrecessionNutation(dpsi, deps, epsa, rb, rp, rbp, rn, rbpn);
16209
16210 }
16211
16212
16213 /**
16214 * Precession-nutation, IAU 2006/2000A models: a multi-purpose function,
16215 * supporting classical (equinox-based) use directly and CIO-based use
16216 * indirectly.
16217 *
16218 *<p>This function is derived from the International Astronomical Union's
16219 * SOFA (Standards Of Fundamental Astronomy) software collection.
16220 *
16221 *<p>Status: support function.
16222 *
16223 *<!-- Given: -->
16224 * @param date1 double TT as a 2-part Julian Date (Note 1)
16225 * @param date2 double TT as a 2-part Julian Date (Note 1)
16226 *
16227 *<!-- Returned: -->
16228 * @return dpsi,deps double <u>returned</u> nutation (Note 2)
16229 * epsa double <u>returned</u> mean obliquity (Note 3)
16230 * rb double[3][3] <u>returned</u> frame bias matrix (Note 4)
16231 * rp double[3][3] <u>returned</u> precession matrix (Note 5)
16232 * rbp double[3][3] <u>returned</u> bias-precession matrix (Note 6)
16233 * rn double[3][3] <u>returned</u> nutation matrix (Note 7)
16234 * rbpn double[3][3] <u>returned</u> GCRS-to-true matrix (Notes 8,9)
16235 *
16236 * <p>Notes:
16237 * <ol>
16238 *
16239 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
16240 * convenient way between the two arguments. For example,
16241 * JD(TT)=2450123.7 could be expressed in any of these ways,
16242 * among others:
16243 *<pre>
16244 * date1 date2
16245 *
16246 * 2450123.7 0.0 (JD method)
16247 * 2451545.0 -1421.3 (J2000 method)
16248 * 2400000.5 50123.2 (MJD method)
16249 * 2450123.5 0.2 (date & time method)
16250 *</pre>
16251 * The JD method is the most natural and convenient to use in
16252 * cases where the loss of several decimal digits of resolution
16253 * is acceptable. The J2000 method is best matched to the way
16254 * the argument is handled internally and will deliver the
16255 * optimum resolution. The MJD method and the date & time methods
16256 * are both good compromises between resolution and convenience.
16257 *
16258 * <li> The nutation components (luni-solar + planetary, IAU 2000A) in
16259 * longitude and obliquity are in radians and with respect to the
16260 * equinox and ecliptic of date. Free core nutation is omitted;
16261 * for the utmost accuracy, use the jauPn06 function, where the
16262 * nutation components are caller-specified.
16263 *
16264 * <li> The mean obliquity is consistent with the IAU 2006 precession.
16265 *
16266 * <li> The matrix rb transforms vectors from GCRS to mean J2000.0 by
16267 * applying frame bias.
16268 *
16269 * <li> The matrix rp transforms vectors from mean J2000.0 to mean of
16270 * date by applying precession.
16271 *
16272 * <li> The matrix rbp transforms vectors from GCRS to mean of date by
16273 * applying frame bias then precession. It is the product rp x rb.
16274 *
16275 * <li> The matrix rn transforms vectors from mean of date to true of
16276 * date by applying the nutation (luni-solar + planetary).
16277 *
16278 * <li> The matrix rbpn transforms vectors from GCRS to true of date
16279 * (CIP/equinox). It is the product rn x rbp, applying frame bias,
16280 * precession and nutation in that order.
16281 *
16282 * <li> The X,Y,Z coordinates of the IAU 2006/2000A Celestial
16283 * Intermediate Pole are elements (1,1-3) of the matrix rbpn.
16284 *
16285 * <li> It is permissible to re-use the same array in the returned
16286 * arguments. The arrays are filled in the stated order.
16287 *</ol>
16288 *<p>Called:<ul>
16289 * <li>{@link #jauNut06a} nutation, IAU 2006/2000A
16290 * <li>{@link #jauPn06} bias/precession/nutation results, IAU 2006
16291 * </ul>
16292 *<p>Reference:
16293 *
16294 * <p>Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
16295 *
16296 *@version 2009 December 18
16297 *
16298 * @since Release 20101201
16299 *
16300 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16301 */
16302 public static PrecessionNutation jauPn06a(double date1, double date2)
16303 {
16304 /* Nutation. */
16305 NutationTerms nut = jauNut06a(date1, date2);
16306
16307 /* Remaining results. */
16308 return jauPn06(date1, date2, nut.dpsi, nut.deps);
16309
16310 }
16311
16312
16313 /**
16314 * Form the matrix of precession-nutation for a given date (including
16315 * frame bias), equinox-based, IAU 2000A model.
16316 *
16317 *<p>This function is derived from the International Astronomical Union's
16318 * SOFA (Standards Of Fundamental Astronomy) software collection.
16319 *
16320 *<p>Status: support function.
16321 *
16322 *<!-- Given: -->
16323 * @param date1 double TT as a 2-part Julian Date (Note 1)
16324 * @param date2 double TT as a 2-part Julian Date (Note 1)
16325 *
16326 *<!-- Returned: -->
16327 * @return rbpn double[3][3] <u>returned</u> classical NPB matrix (Note 2)
16328 *
16329 * <p>Notes:
16330 * <ol>
16331 *
16332 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
16333 * convenient way between the two arguments. For example,
16334 * JD(TT)=2450123.7 could be expressed in any of these ways,
16335 * among others:
16336 *<pre>
16337 * date1 date2
16338 *
16339 * 2450123.7 0.0 (JD method)
16340 * 2451545.0 -1421.3 (J2000 method)
16341 * 2400000.5 50123.2 (MJD method)
16342 * 2450123.5 0.2 (date & time method)
16343 *</pre>
16344 * The JD method is the most natural and convenient to use in
16345 * cases where the loss of several decimal digits of resolution
16346 * is acceptable. The J2000 method is best matched to the way
16347 * the argument is handled internally and will deliver the
16348 * optimum resolution. The MJD method and the date & time methods
16349 * are both good compromises between resolution and convenience.
16350 *
16351 * <li> The matrix operates in the sense V(date) = rbpn * V(GCRS), where
16352 * the p-vector V(date) is with respect to the true equatorial triad
16353 * of date date1+date2 and the p-vector V(GCRS) is with respect to
16354 * the Geocentric Celestial Reference System (IAU, 2000).
16355 *
16356 * <li> A faster, but slightly less accurate result (about 1 mas), can be
16357 * obtained by using instead the jauPnm00b function.
16358 *</ol>
16359 *<p>Called:<ul>
16360 * <li>{@link #jauPn00a} bias/precession/nutation, IAU 2000A
16361 * </ul>
16362 *<p>Reference:
16363 *
16364 * IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc.
16365 * 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6.
16366 * (2000)
16367 *
16368 *@version 2009 December 21
16369 *
16370 * @since Release 20101201
16371 *
16372 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16373 */
16374 public static double[][] jauPnm00a(double date1, double date2)
16375 {
16376
16377 /* Obtain the required matrix (discarding other results). */
16378 PrecessionNutation pn = jauPn00a(date1, date2);
16379 return pn.rbpn;
16380
16381 }
16382
16383
16384 /**
16385 * Form the matrix of precession-nutation for a given date (including
16386 * frame bias), equinox-based, IAU 2000B model.
16387 *
16388 *<p>This function is derived from the International Astronomical Union's
16389 * SOFA (Standards Of Fundamental Astronomy) software collection.
16390 *
16391 *<p>Status: support function.
16392 *
16393 *<!-- Given: -->
16394 * @param date1 double TT as a 2-part Julian Date (Note 1)
16395 * @param date2 double TT as a 2-part Julian Date (Note 1)
16396 *
16397 *<!-- Returned: -->
16398 * @return rbpn double[3][3] <u>returned</u> bias-precession-nutation matrix (Note 2)
16399 *
16400 * <p>Notes:
16401 * <ol>
16402 *
16403 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
16404 * convenient way between the two arguments. For example,
16405 * JD(TT)=2450123.7 could be expressed in any of these ways,
16406 * among others:
16407 *<pre>
16408 * date1 date2
16409 *
16410 * 2450123.7 0.0 (JD method)
16411 * 2451545.0 -1421.3 (J2000 method)
16412 * 2400000.5 50123.2 (MJD method)
16413 * 2450123.5 0.2 (date & time method)
16414 *</pre>
16415 * The JD method is the most natural and convenient to use in
16416 * cases where the loss of several decimal digits of resolution
16417 * is acceptable. The J2000 method is best matched to the way
16418 * the argument is handled internally and will deliver the
16419 * optimum resolution. The MJD method and the date & time methods
16420 * are both good compromises between resolution and convenience.
16421 *
16422 * <li> The matrix operates in the sense V(date) = rbpn * V(GCRS), where
16423 * the p-vector V(date) is with respect to the true equatorial triad
16424 * of date date1+date2 and the p-vector V(GCRS) is with respect to
16425 * the Geocentric Celestial Reference System (IAU, 2000).
16426 *
16427 * <li> The present function is faster, but slightly less accurate (about
16428 * 1 mas), than the jauPnm00a function.
16429 *</ol>
16430 *<p>Called:<ul>
16431 * <li>{@link #jauPn00b} bias/precession/nutation, IAU 2000B
16432 * </ul>
16433 *<p>Reference:
16434 *
16435 * IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc.
16436 * 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6.
16437 * (2000)
16438 *
16439 *@version 2009 December 21
16440 *
16441 * @since Release 20101201
16442 *
16443 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16444 */
16445 public static double[][] jauPnm00b(double date1, double date2)
16446 {
16447
16448 /* Obtain the required matrix (discarding other results). */
16449 PrecessionNutation pn = jauPn00b(date1, date2);
16450
16451 return pn.rbpn;
16452
16453 }
16454
16455
16456 /**
16457 * Form the matrix of precession-nutation for a given date (including
16458 * frame bias), IAU 2006 precession and IAU 2000A nutation models.
16459 *
16460 *<p>This function is derived from the International Astronomical Union's
16461 * SOFA (Standards Of Fundamental Astronomy) software collection.
16462 *
16463 *<p>Status: support function.
16464 *
16465 *<!-- Given: -->
16466 * @param date1 double TT as a 2-part Julian Date (Note 1)
16467 * @param date2 double TT as a 2-part Julian Date (Note 1)
16468 *
16469 *<!-- Returned: -->
16470 * @return rnpb double[3][3] <u>returned</u> bias-precession-nutation matrix (Note 2)
16471 *
16472 * <p>Notes:
16473 * <ol>
16474 *
16475 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
16476 * convenient way between the two arguments. For example,
16477 * JD(TT)=2450123.7 could be expressed in any of these ways,
16478 * among others:
16479 *<pre>
16480 * date1 date2
16481 *
16482 * 2450123.7 0.0 (JD method)
16483 * 2451545.0 -1421.3 (J2000 method)
16484 * 2400000.5 50123.2 (MJD method)
16485 * 2450123.5 0.2 (date & time method)
16486 *</pre>
16487 * The JD method is the most natural and convenient to use in
16488 * cases where the loss of several decimal digits of resolution
16489 * is acceptable. The J2000 method is best matched to the way
16490 * the argument is handled internally and will deliver the
16491 * optimum resolution. The MJD method and the date & time methods
16492 * are both good compromises between resolution and convenience.
16493 *
16494 * <li> The matrix operates in the sense V(date) = rnpb * V(GCRS), where
16495 * the p-vector V(date) is with respect to the true equatorial triad
16496 * of date date1+date2 and the p-vector V(GCRS) is with respect to
16497 * the Geocentric Celestial Reference System (IAU, 2000).
16498 *</ol>
16499 *<p>Called:<ul>
16500 * <li>{@link #jauPfw06} bias-precession F-W angles, IAU 2006
16501 * <li>{@link #jauNut06a} nutation, IAU 2006/2000A
16502 * <li>{@link #jauFw2m} F-W angles to r-matrix
16503 * </ul>
16504 *<p>Reference:
16505 *
16506 * <p>Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855.
16507 *
16508 *@version 2009 December 21
16509 *
16510 * @since Release 20101201
16511 *
16512 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16513 */
16514 public static double[][] jauPnm06a(double date1, double date2)
16515 {
16516
16517 /* Fukushima-Williams angles for frame bias and precession. */
16518 FWPrecessionAngles fw = jauPfw06(date1, date2);
16519
16520 /* Nutation components. */
16521 NutationTerms nut = jauNut06a(date1, date2);
16522
16523 /* Equinox based nutation x precession x bias matrix. */
16524 double[][] rnpb = jauFw2m(fw.gamb, fw.phib, fw.psib + nut.dpsi, fw.epsa + nut.deps);
16525
16526 return rnpb;
16527
16528 }
16529
16530
16531 /**
16532 * Form the matrix of precession/nutation for a given date, IAU 1976
16533 * precession model, IAU 1980 nutation model.
16534 *
16535 *<p>This function is derived from the International Astronomical Union's
16536 * SOFA (Standards Of Fundamental Astronomy) software collection.
16537 *
16538 *<p>Status: support function.
16539 *
16540 *<!-- Given: -->
16541 * @param date1 double TDB date (Note 1)
16542 * @param date2 double TDB date (Note 1)
16543 *
16544 *<!-- Returned: -->
16545 * @return rmatpn double[3][3] <u>returned</u> combined precession/nutation matrix
16546 *
16547 * <p>Notes:
16548 * <ol>
16549 *
16550 * <li> The TDB date date1+date2 is a Julian Date, apportioned in any
16551 * convenient way between the two arguments. For example,
16552 * JD(TDB)=2450123.7 could be expressed in any of these ways,
16553 * among others:
16554 *<pre>
16555 * date1 date2
16556 *
16557 * 2450123.7 0.0 (JD method)
16558 * 2451545.0 -1421.3 (J2000 method)
16559 * 2400000.5 50123.2 (MJD method)
16560 * 2450123.5 0.2 (date & time method)
16561 *</pre>
16562 * The JD method is the most natural and convenient to use in
16563 * cases where the loss of several decimal digits of resolution
16564 * is acceptable. The J2000 method is best matched to the way
16565 * the argument is handled internally and will deliver the
16566 * optimum resolution. The MJD method and the date & time methods
16567 * are both good compromises between resolution and convenience.
16568 *
16569 * <li> The matrix operates in the sense V(date) = rmatpn * V(J2000),
16570 * where the p-vector V(date) is with respect to the true equatorial
16571 * triad of date date1+date2 and the p-vector V(J2000) is with
16572 * respect to the mean equatorial triad of epoch J2000.0.
16573 *</ol>
16574 *<p>Called:<ul>
16575 * <li>{@link #jauPmat76} precession matrix, IAU 1976
16576 * <li>{@link #jauNutm80} nutation matrix, IAU 1980
16577 * <li>{@link #jauRxr} product of two r-matrices
16578 * </ul>
16579 *<p>Reference:
16580 *
16581 * <p>Explanatory Supplement to the Astronomical Almanac,
16582 * P. Kenneth Seidelmann (ed), University Science Books (1992),
16583 * Section 3.3 (p145).
16584 *
16585 *@version 2010 January 23
16586 *
16587 * @since Release 20101201
16588 *
16589 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16590 */
16591 public static double[][] jauPnm80(double date1, double date2)
16592 {
16593 double rmatp[][] = new double[3][3], rmatn[][] = new double[3][3];
16594
16595
16596 /* Precession matrix, J2000.0 to date. */
16597 rmatp = jauPmat76(date1, date2 );
16598
16599 /* Nutation matrix. */
16600 rmatn = jauNutm80(date1, date2);
16601
16602 /* Combine the matrices: PN = N x P. */
16603 double[][] rmatpn = jauRxr(rmatn, rmatp);
16604
16605 return rmatpn;
16606
16607 }
16608
16609
16610 /**
16611 * Form the matrix of polar motion for a given date, IAU 2000.
16612 *
16613 *<p>This function is derived from the International Astronomical Union's
16614 * SOFA (Standards Of Fundamental Astronomy) software collection.
16615 *
16616 *<p>Status: support function.
16617 *
16618 *<!-- Given: -->
16619 * @param xp double coordinates of the pole (radians, Note 1)
16620 * @param yp double coordinates of the pole (radians, Note 1)
16621 * @param sp double the TIO locator s' (radians, Note 2)
16622 *
16623 *<!-- Returned: -->
16624 * @return double[3][3] <u>returned</u> polar-motion matrix (Note 3)
16625 *
16626 * <p>Notes:
16627 * <ol>
16628 *
16629 * <li> The arguments xp and yp are the coordinates (in radians) of the
16630 * Celestial Intermediate Pole with respect to the International
16631 * Terrestrial Reference System (see IERS Conventions 2003),
16632 * measured along the meridians to 0 and 90 deg west respectively.
16633 *
16634 * <li> The argument sp is the TIO locator s', in radians, which
16635 * positions the Terrestrial Intermediate Origin on the equator. It
16636 * is obtained from polar motion observations by numerical
16637 * integration, and so is in essence unpredictable. However, it is
16638 * dominated by a secular drift of about 47 microarcseconds per
16639 * century, and so can be taken into account by using s' = -47*t,
16640 * where t is centuries since J2000.0. The function jauSp00
16641 * implements this approximation.
16642 *
16643 * <li> The matrix operates in the sense V(TRS) = rpom * V(CIP), meaning
16644 * that it is the final rotation when computing the pointing
16645 * direction to a celestial source.
16646 *</ol>
16647 *<p>Called:<ul>
16648 * <li>{@link #jauIr} initialize r-matrix to identity
16649 * <li>{@link #jauRz} rotate around Z-axis
16650 * <li>{@link #jauRy} rotate around Y-axis
16651 * <li>{@link #jauRx} rotate around X-axis
16652 * </ul>
16653 *<p>Reference:
16654 *
16655 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
16656 * IERS Technical Note No. 32, BKG (2004)
16657 *
16658 *@version 2009 December 17
16659 *
16660 * @since Release 20101201
16661 *
16662 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16663 */
16664 public static double[][] jauPom00(double xp, double yp, double sp)
16665 {
16666
16667 /* Construct the matrix. */
16668 double rpom[][] = new double[3][3];
16669 jauIr(rpom);
16670 jauRz(sp, rpom);
16671 jauRy(-xp, rpom);
16672 jauRx(-yp, rpom);
16673
16674 return rpom;
16675
16676 }
16677
16678
16679 /**
16680 * P-vector addition.
16681 *
16682 *<p>This function is derived from the International Astronomical Union's
16683 * SOFA (Standards Of Fundamental Astronomy) software collection.
16684 *
16685 *<p>Status: vector/matrix support function.
16686 *
16687 *<!-- Given: -->
16688 * @param a double[3] first p-vector
16689 * @param b double[3] second p-vector
16690 *
16691 *<!-- Returned: -->
16692 * @return apb double[3] <u>returned</u> a + b
16693 *
16694 * Note:
16695 * It is permissible to re-use the same array for any of the
16696 * arguments.
16697 *
16698 *@version 2008 November 18
16699 *
16700 * @since Release 20101201
16701 *
16702 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16703 */
16704 public static double[] jauPpp(double a[] , double b[] )
16705 {
16706 double apb[] = new double[3];
16707 apb[0] = a[0] + b[0];
16708 apb[1] = a[1] + b[1];
16709 apb[2] = a[2] + b[2];
16710
16711 return apb;
16712
16713 }
16714
16715
16716 /**
16717 * P-vector plus scaled p-vector.
16718 *
16719 *<p>This function is derived from the International Astronomical Union's
16720 * SOFA (Standards Of Fundamental Astronomy) software collection.
16721 *
16722 *<p>Status: vector/matrix support function.
16723 *
16724 *<!-- Given: -->
16725 * @param a double[3] first p-vector
16726 * @param s double scalar (multiplier for b)
16727 * @param b double[3] second p-vector
16728 *
16729 *<!-- Returned: -->
16730 * @return apsb double[3] <u>returned</u> a + s*b
16731 *
16732 * Note:
16733 * It is permissible for any of a, b and apsb to be the same array.
16734 *
16735 *<p>Called:<ul>
16736 * <li>{@link #jauSxp} multiply p-vector by scalar
16737 * <li>{@link #jauPpp} p-vector plus p-vector
16738 * </ul>
16739 *@version 2008 November 18
16740 *
16741 * @since Release 20101201
16742 *
16743 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16744 */
16745 static double[] jauPpsp(double a[] , double s, double b[] )
16746 {
16747 double sb[] = new double[3], apsb[];
16748
16749
16750 /* s*b. */
16751 sb = jauSxp(s,b);
16752
16753 /* a + s*b. */
16754 apsb = jauPpp(a, sb);
16755
16756 return apsb;
16757
16758 }
16759
16760 /**
16761 * Precession correction terms.
16762 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 4 Feb 2010
16763 *
16764 * @since AIDA Stage 1
16765 */
16766 public static class PrecessionDeltaTerms {
16767 /** precession correction in longitude */
16768 public double dpsipr;
16769 /** precession correction in obliquity */
16770 public double depspr;
16771 public PrecessionDeltaTerms(double dpsipr, double depspr) {
16772 this.dpsipr = dpsipr;
16773 this.depspr = depspr;
16774 }
16775 }
16776
16777 /**
16778 * Precession-rate part of the IAU 2000 precession-nutation models
16779 * (part of MHB2000).
16780 *
16781 *<p>This function is derived from the International Astronomical Union's
16782 * SOFA (Standards Of Fundamental Astronomy) software collection.
16783 *
16784 *<p>Status: canonical model.
16785 *
16786 *<!-- Given: -->
16787 * @param date1 double TT as a 2-part Julian Date (Note 1)
16788 * @param date2 double TT as a 2-part Julian Date (Note 1)
16789 *
16790 *<!-- Returned: -->
16791 * @param dpsipr double <u>returned</u> precession corrections (Notes 2,3)
16792 * @param depspr double <u>returned</u> precession corrections (Notes 2,3)
16793 *
16794 * <p>Notes:
16795 * <ol>
16796 *
16797 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
16798 * convenient way between the two arguments. For example,
16799 * JD(TT)=2450123.7 could be expressed in any of these ways,
16800 * among others:
16801 *<pre>
16802 * date1 date2
16803 *
16804 * 2450123.7 0.0 (JD method)
16805 * 2451545.0 -1421.3 (J2000 method)
16806 * 2400000.5 50123.2 (MJD method)
16807 * 2450123.5 0.2 (date & time method)
16808 *</pre>
16809 * The JD method is the most natural and convenient to use in
16810 * cases where the loss of several decimal digits of resolution
16811 * is acceptable. The J2000 method is best matched to the way
16812 * the argument is handled internally and will deliver the
16813 * optimum resolution. The MJD method and the date & time methods
16814 * are both good compromises between resolution and convenience.
16815 *
16816 * <li> The precession adjustments are expressed as "nutation
16817 * components", corrections in longitude and obliquity with respect
16818 * to the J2000.0 equinox and ecliptic.
16819 *
16820 * <li> Although the precession adjustments are stated to be with respect
16821 * to Lieske et al. (1977), the MHB2000 model does not specify which
16822 * set of Euler angles are to be used and how the adjustments are to
16823 * be applied. The most literal and straightforward procedure is to
16824 * adopt the 4-rotation epsilon_0, psi_A, omega_A, xi_A option, and
16825 * to add dpsipr to psi_A and depspr to both omega_A and eps_A.
16826 *
16827 * <li> This is an implementation of one aspect of the IAU 2000A nutation
16828 * model, formally adopted by the IAU General Assembly in 2000,
16829 * namely MHB2000 (Mathews et al. 2002).
16830 *
16831 *<p>References:
16832 *
16833 * <p>Lieske, J.H., Lederle, T., Fricke, W. & Morando, B., "Expressions
16834 * for the precession quantities based upon the IAU (1976) System of
16835 * Astronomical Constants", Astron.Astrophys., 58, 1-16 (1977)
16836 *
16837 * <p>Mathews, P.M., Herring, T.A., Buffet, B.A., "Modeling of nutation
16838 * and precession New nutation series for nonrigid Earth and
16839 * insights into the Earth's interior", J.Geophys.Res., 107, B4,
16840 * 2002. The MHB2000 code itself was obtained on 9th September 2002
16841 * from ftp://maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
16842 *
16843 * <p>Wallace, P.T., "Software for Implementing the IAU 2000
16844 * Resolutions", in IERS Workshop 5.1 (2002).
16845 *
16846 *@version 2009 December 17
16847 *
16848 * @since Release 20101201
16849 *
16850 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16851 */
16852 static PrecessionDeltaTerms jauPr00(double date1, double date2)
16853 {
16854 double t;
16855
16856 /* Precession and obliquity corrections (radians per century) */
16857 final double PRECOR = -0.29965 * DAS2R,
16858 OBLCOR = -0.02524 * DAS2R;
16859
16860
16861 /* Interval between fundamental epoch J2000.0 and given date (JC). */
16862 t = ((date1 - DJ00) + date2) / DJC;
16863
16864 /* Precession rate contributions with respect to IAU 1976/80. */
16865 double dpsipr = PRECOR * t;
16866 double depspr = OBLCOR * t;
16867
16868 return new PrecessionDeltaTerms(dpsipr, depspr);
16869
16870 }
16871
16872 /**
16873 * Euler Angles.
16874 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 4 Feb 2010
16875 *
16876 * @since AIDA Stage 1
16877 */
16878 public static class EulerAngles {
16879 /** 1st rotation: radians cw around z */
16880 public double zeta;
16881 /** 3rd rotation: radians cw around z */
16882 public double z;
16883 /** 2nd rotation: radians ccw around y */
16884 public double theta;
16885 public EulerAngles(double zeta, double z, double theta){
16886 this.zeta = zeta;
16887 this.z = z;
16888 this.theta = theta;
16889 }
16890 }
16891
16892 /**
16893 * IAU 1976 precession model.
16894 *
16895 * This function forms the three Euler angles which implement general
16896 * precession between two epochs, using the IAU 1976 model (as for
16897 * the FK5 catalog).
16898 *
16899 *<p>This function is derived from the International Astronomical Union's
16900 * SOFA (Standards Of Fundamental Astronomy) software collection.
16901 *
16902 *<p>Status: canonical model.
16903 *
16904 *<!-- Given: -->
16905 * @param ep01 double TDB starting epoch (Note 1)
16906 * @param ep02 double TDB starting epoch (Note 1)
16907 * @param ep11 double TDB ending epoch (Note 1)
16908 * @param ep12 double TDB ending epoch (Note 1)
16909 *
16910 *<!-- Returned: -->
16911 * @param zeta double <u>returned</u> 1st rotation: radians cw around z
16912 * @param z double <u>returned</u> 3rd rotation: radians cw around z
16913 * @param theta double <u>returned</u> 2nd rotation: radians ccw around y
16914 *
16915 * <p>Notes:
16916 * <ol>
16917 *
16918 * <li> The epochs ep01+ep02 and ep11+ep12 are Julian Dates, apportioned
16919 * in any convenient way between the arguments epn1 and epn2. For
16920 * example, JD(TDB)=2450123.7 could be expressed in any of these
16921 * ways, among others:
16922 *
16923 * epn1 epn2
16924 *
16925 * 2450123.7 0.0 (JD method)
16926 * 2451545.0 -1421.3 (J2000 method)
16927 * 2400000.5 50123.2 (MJD method)
16928 * 2450123.5 0.2 (date & time method)
16929 *</pre>
16930 * The JD method is the most natural and convenient to use in cases
16931 * where the loss of several decimal digits of resolution is
16932 * acceptable. The J2000 method is best matched to the way the
16933 * argument is handled internally and will deliver the optimum
16934 * optimum resolution. The MJD method and the date & time methods
16935 * are both good compromises between resolution and convenience.
16936 * The two epochs may be expressed using different methods, but at
16937 * the risk of losing some resolution.
16938 *
16939 * <li> The accumulated precession angles zeta, z, theta are expressed
16940 * through canonical polynomials which are valid only for a limited
16941 * time span. In addition, the IAU 1976 precession rate is known to
16942 * be imperfect. The absolute accuracy of the present formulation
16943 * is better than 0.1 arcsec from 1960AD to 2040AD, better than
16944 * 1 arcsec from 1640AD to 2360AD, and remains below 3 arcsec for
16945 * the whole of the period 500BC to 3000AD. The errors exceed
16946 * 10 arcsec outside the range 1200BC to 3900AD, exceed 100 arcsec
16947 * outside 4200BC to 5600AD and exceed 1000 arcsec outside 6800BC to
16948 * 8200AD.
16949 *
16950 * <li> The three angles are returned in the conventional order, which
16951 * is not the same as the order of the corresponding Euler
16952 * rotations. The precession matrix is
16953 * R_3(-z) x R_2(+theta) x R_3(-zeta).
16954 *
16955 *<p>Reference:
16956 *
16957 * <p>Lieske, J.H., 1979, Astron.Astrophys. 73, 282, equations
16958 * (6) & (7), p283.
16959 *
16960 *@version 2009 December 17
16961 *
16962 * @since Release 20101201
16963 *
16964 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16965 */
16966 static EulerAngles jauPrec76(double ep01, double ep02, double ep11, double ep12)
16967 {
16968 double t0, t, tas2r, w;
16969
16970
16971 /* Interval between fundamental epoch J2000.0 and start epoch (JC). */
16972 t0 = ((ep01 - DJ00) + ep02) / DJC;
16973
16974 /* Interval over which precession required (JC). */
16975 t = ((ep11 - ep01) + (ep12 - ep02)) / DJC;
16976
16977 /* Euler angles. */
16978 tas2r = t * DAS2R;
16979 w = 2306.2181 + (1.39656 - 0.000139 * t0) * t0;
16980
16981 double zeta = (w + ((0.30188 - 0.000344 * t0) + 0.017998 * t) * t) * tas2r;
16982
16983 double z = (w + ((1.09468 + 0.000066 * t0) + 0.018203 * t) * t) * tas2r;
16984
16985 double theta = ((2004.3109 + (-0.85330 - 0.000217 * t0) * t0)
16986 + ((-0.42665 - 0.000217 * t0) - 0.041833 * t) * t) * tas2r;
16987
16988 return new EulerAngles(zeta, z, theta);
16989
16990 }
16991
16992
16993 /**
16994 * Discard velocity component of a pv-vector.
16995 *
16996 *<p>This function is derived from the International Astronomical Union's
16997 * SOFA (Standards Of Fundamental Astronomy) software collection.
16998 *
16999 *<p>Status: vector/matrix support function.
17000 *
17001 *<!-- Given: -->
17002 * @param pv double[2][3] pv-vector
17003 *
17004 *<!-- Returned: -->
17005 * @return p double[3] <u>returned</u> p-vector
17006 *
17007 *<p>Called:<ul>
17008 * <li>{@link #jauCp} copy p-vector
17009 * </ul>
17010 *@version 2008 May 11
17011 *
17012 * @since Release 20101201
17013 *
17014 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17015 */
17016 public static double[] jauPv2p(double pv[][] )
17017 {
17018 double p[] = new double[3];
17019 jauCp(pv[0], p);
17020
17021 return p;
17022
17023 }
17024
17025
17026 /**
17027 * A position and velocity expressed in spherical polar coordinates.
17028 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 4 Feb 2010
17029 *
17030 * @since AIDA Stage 1
17031 */
17032 public static class SphericalPositionVelocity {
17033 public SphericalPosition pos;
17034 public SphericalPosition vel;
17035 public SphericalPositionVelocity( double theta, double phi, double r,
17036 double td, double pd, double rd) {
17037 pos = new SphericalPosition(theta, phi, r);
17038 vel = new SphericalPosition(td,pd,rd);
17039 }
17040 }
17041 /**
17042 * Convert position/velocity from Cartesian to spherical coordinates.
17043 *
17044 *<p>This function is derived from the International Astronomical Union's
17045 * SOFA (Standards Of Fundamental Astronomy) software collection.
17046 *
17047 *<p>Status: vector/matrix support function.
17048 *
17049 *<!-- Given: -->
17050 * @param pv double[2][3] pv-vector
17051 *
17052 *<!-- Returned: -->
17053 * @return theta double <u>returned</u> longitude angle (radians)
17054 * phi double <u>returned</u> latitude angle (radians)
17055 * r double <u>returned</u> radial distance
17056 * td double <u>returned</u> rate of change of theta
17057 * pd double <u>returned</u> rate of change of phi
17058 * rd double <u>returned</u> rate of change of r
17059 *
17060 * <p>Notes:
17061 * <ol>
17062 *
17063 * <li> If the position part of pv is null, theta, phi, td and pd
17064 * are indeterminate. This is handled by extrapolating the
17065 * position through unit time by using the velocity part of
17066 * pv. This moves the origin without changing the direction
17067 * of the velocity component. If the position and velocity
17068 * components of pv are both null, zeroes are returned for all
17069 * six results.
17070 *
17071 * <li> If the position is a pole, theta, td and pd are indeterminate.
17072 * In such cases zeroes are returned for all three.
17073 *</ol>
17074 *@version 2008 October 28
17075 *
17076 * @since Release 20101201
17077 *
17078 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17079 */
17080 public static SphericalPositionVelocity jauPv2s(double pv[][])
17081 {
17082 double x, y, z, xd, yd, zd, rxy2, rxy, r2, rtrue, rw, xyp;
17083 double theta, phi, r, td, pd, rd;
17084
17085 /* Components of position/velocity vector. */
17086 x = pv[0][0];
17087 y = pv[0][1];
17088 z = pv[0][2];
17089 xd = pv[1][0];
17090 yd = pv[1][1];
17091 zd = pv[1][2];
17092
17093 /* Component of r in XY plane squared. */
17094 rxy2 = x*x + y*y;
17095
17096 /* Modulus squared. */
17097 r2 = rxy2 + z*z;
17098
17099 /* Modulus. */
17100 rtrue = sqrt(r2);
17101
17102 /* If null vector, move the origin along the direction of movement. */
17103 rw = rtrue;
17104 if (rtrue == 0.0) {
17105 x = xd;
17106 y = yd;
17107 z = zd;
17108 rxy2 = x*x + y*y;
17109 r2 = rxy2 + z*z;
17110 rw = sqrt(r2);
17111 }
17112
17113 /* Position and velocity in spherical coordinates. */
17114 rxy = sqrt(rxy2);
17115 xyp = x*xd + y*yd;
17116 if (rxy2 != 0.0) {
17117 theta = atan2(y, x);
17118 phi = atan2(z, rxy);
17119 td = (x*yd - y*xd) / rxy2;
17120 pd = (zd*rxy2 - z*xyp) / (r2*rxy);
17121 } else {
17122 theta = 0.0;
17123 phi = (z != 0.0) ? atan2(z, rxy) : 0.0;
17124 td = 0.0;
17125 pd = 0.0;
17126 }
17127 r = rtrue;
17128 rd = (rw != 0.0) ? (xyp + z*zd) / rw : 0.0;
17129
17130 return new SphericalPositionVelocity(theta, phi, r, td, pd, rd);
17131
17132 }
17133
17134
17135 /**
17136 * Inner (=scalar=dot) product of two pv-vectors.
17137 *
17138 *<p>This function is derived from the International Astronomical Union's
17139 * SOFA (Standards Of Fundamental Astronomy) software collection.
17140 *
17141 *<p>Status: vector/matrix support function.
17142 *
17143 *<!-- Given: -->
17144 * @param a double[2][3] first pv-vector
17145 * @param b double[2][3] second pv-vector
17146 *
17147 *<!-- Returned: -->
17148 * @return adb double[2] <u>returned</u> a . b (see note)
17149 *
17150 * Note:
17151 *
17152 * If the position and velocity components of the two pv-vectors are
17153 * ( ap, av ) and ( bp, bv ), the result, a . b, is the pair of
17154 * numbers ( ap . bp , ap . bv + av . bp ). The two numbers are the
17155 * dot-product of the two p-vectors and its derivative.
17156 *
17157 *<p>Called:<ul>
17158 * <li>{@link #jauPdp} scalar product of two p-vectors
17159 * </ul>
17160 *@version 2008 May 22
17161 *
17162 * @since Release 20101201
17163 *
17164 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17165 */
17166 public static double[] jauPvdpv(double a[][], double b[][] )
17167 {
17168 double adbd, addb, adb[] = new double[2];
17169
17170
17171 /* a . b = constant part of result. */
17172 adb[0] = jauPdp(a[0], b[0]);
17173
17174 /* a . bdot */
17175 adbd = jauPdp(a[0], b[1]);
17176
17177 /* adot . b */
17178 addb = jauPdp(a[1], b[0]);
17179
17180 /* Velocity part of result. */
17181 adb[1] = adbd + addb;
17182
17183 return adb;
17184
17185 }
17186
17187
17188 /**
17189 * Modulus of pv-vector.
17190 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 4 Feb 2010
17191 *
17192 * @since AIDA Stage 1
17193 */
17194 public static class PVModulus{
17195 public double r;
17196 public double s;
17197 public PVModulus( double r, double s){
17198 this.r = r;
17199 this.s = s;
17200 }
17201 }
17202 /**
17203 * Modulus of pv-vector.
17204 *
17205 *<p>This function is derived from the International Astronomical Union's
17206 * SOFA (Standards Of Fundamental Astronomy) software collection.
17207 *
17208 *<p>Status: vector/matrix support function.
17209 *
17210 *<!-- Given: -->
17211 * @param pv double[2][3] pv-vector
17212 *
17213 *<!-- Returned: -->
17214 * @return modulus of position component,
17215 * modulus of velocity component
17216 *
17217 *<p>Called:<ul>
17218 * <li>{@link #jauPm} modulus of p-vector
17219 * </ul>
17220 *@version 2008 May 22
17221 *
17222 * @since Release 20101201
17223 *
17224 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17225 */
17226 public static PVModulus jauPvm(double pv[][])
17227 {
17228 /* Distance. */
17229 double r = jauPm(pv[0]);
17230
17231 /* Speed. */
17232 double s = jauPm(pv[1]);
17233
17234 return new PVModulus(r, s);
17235
17236 }
17237
17238
17239 /**
17240 * Subtract one pv-vector from another.
17241 *
17242 *<p>This function is derived from the International Astronomical Union's
17243 * SOFA (Standards Of Fundamental Astronomy) software collection.
17244 *
17245 *<p>Status: vector/matrix support function.
17246 *
17247 *<!-- Given: -->
17248 * @param a double[2][3] first pv-vector
17249 * @param b double[2][3] second pv-vector
17250 *
17251 *<!-- Returned: -->
17252 * @return double[2][3] <u>returned</u> a - b
17253 *
17254 * Note:
17255 * It is permissible to re-use the same array for any of the
17256 * arguments.
17257 *
17258 *<p>Called:<ul>
17259 * <li>{@link #jauPmp} p-vector minus p-vector
17260 * </ul>
17261 *@version 2008 November 18
17262 *
17263 * @since Release 20101201
17264 *
17265 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17266 */
17267 public static double[][] jauPvmpv(double a[][], double b[][])
17268 {
17269 double amb[][] = new double[2][3];
17270 amb[0] = jauPmp(a[0], b[0]);
17271 amb[1] = jauPmp(a[1], b[1]);
17272
17273 return amb;
17274
17275 }
17276
17277
17278 /**
17279 * Add one pv-vector to another.
17280 *
17281 *<p>This function is derived from the International Astronomical Union's
17282 * SOFA (Standards Of Fundamental Astronomy) software collection.
17283 *
17284 *<p>Status: vector/matrix support function.
17285 *
17286 *<!-- Given: -->
17287 * @param a double[2][3] first pv-vector
17288 * @param b double[2][3] second pv-vector
17289 *
17290 *<!-- Returned: -->
17291 * @return apb double[2][3] <u>returned</u> a + b
17292 *
17293 * Note:
17294 * It is permissible to re-use the same array for any of the
17295 * arguments.
17296 *
17297 *<p>Called:<ul>
17298 * <li>{@link #jauPpp} p-vector plus p-vector
17299 * </ul>
17300 *@version 2008 November 18
17301 *
17302 * @since Release 20101201
17303 *
17304 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17305 */
17306 public static double[][] jauPvppv(double a[][], double b[][])
17307 {
17308 double apb[][] = new double[2][3];
17309 apb[0] = jauPpp(a[0], b[0]);
17310 apb[1] = jauPpp(a[1], b[1]);
17311
17312 return apb;
17313
17314 }
17315
17316
17317 /**
17318 * Typical catalogue coordinates. i.e. Position, proper motion, parallax and radial velocity.
17319 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 4 Feb 2010
17320 *
17321 * @since AIDA Stage 1
17322 */
17323 public static class CatalogCoords {
17324 /** position (radians) */
17325 public SphericalCoordinate pos;
17326 /** proper motion (radians/year)*/
17327 public SphericalCoordinate pm;
17328 /** parallax (arcsec) */
17329 public double px;
17330 /** radial velocity (km/s, positive = receding) */
17331 public double rv;
17332
17333 public CatalogCoords(double ra, double dec,
17334 double pmr, double pmd, double px, double rv) {
17335 this.pos = new SphericalCoordinate(ra, dec);
17336 this.pm = new SphericalCoordinate(pmr, pmd);
17337 this.px = px;
17338 this.rv = rv;
17339 }
17340 }
17341 /**
17342 * Convert star position+velocity vector to catalog coordinates.
17343 *
17344 *<p>This function is derived from the International Astronomical Union's
17345 * SOFA (Standards Of Fundamental Astronomy) software collection.
17346 *
17347 *<p>Status: support function.
17348 *
17349 * Given (Note 1):
17350 * pv double[2][3] pv-vector (AU, AU/day)
17351 *
17352 * Returned (Note 2):
17353 * ra double right ascension (radians)
17354 * dec double declination (radians)
17355 * pmr double RA proper motion (radians/year)
17356 * pmd double Dec proper motion (radians/year)
17357 * px double parallax (arcsec)
17358 * rv double radial velocity (km/s, positive = receding)
17359 *
17360 * <!-- Returned (function value): -->
17361 * @return int status:
17362 * 0 = OK
17363 * -1 = superluminal speed (Note 5)
17364 * -2 = null position vector
17365 *
17366 * <p>Notes:
17367 * <ol>
17368 *
17369 * <li> The specified pv-vector is the coordinate direction (and its rate
17370 * of change) for the date at which the light leaving the star
17371 * reached the solar-system barycenter.
17372 *
17373 * <li> The star data returned by this function are "observables" for an
17374 * imaginary observer at the solar-system barycenter. Proper motion
17375 * and radial velocity are, strictly, in terms of barycentric
17376 * coordinate time, TCB. For most practical applications, it is
17377 * permissible to neglect the distinction between TCB and ordinary
17378 * "proper" time on Earth (TT/TAI). The result will, as a rule, be
17379 * limited by the intrinsic accuracy of the proper-motion and
17380 * radial-velocity data; moreover, the supplied pv-vector is likely
17381 * to be merely an intermediate result (for example generated by the
17382 * function jauStarpv), so that a change of time unit will cancel
17383 * out overall.
17384 *
17385 * In accordance with normal star-catalog conventions, the object's
17386 * right ascension and declination are freed from the effects of
17387 * secular aberration. The frame, which is aligned to the catalog
17388 * equator and equinox, is Lorentzian and centered on the SSB.
17389 *
17390 * Summarizing, the specified pv-vector is for most stars almost
17391 * identical to the result of applying the standard geometrical
17392 * "space motion" transformation to the catalog data. The
17393 * differences, which are the subject of the Stumpff paper cited
17394 * below, are:
17395 *
17396 * (i) In stars with significant radial velocity and proper motion,
17397 * the constantly changing light-time distorts the apparent proper
17398 * motion. Note that this is a classical, not a relativistic,
17399 * effect.
17400 *
17401 * (ii) The transformation complies with special relativity.
17402 *
17403 * <li> Care is needed with units. The star coordinates are in radians
17404 * and the proper motions in radians per Julian year, but the
17405 * parallax is in arcseconds; the radial velocity is in km/s, but
17406 * the pv-vector result is in AU and AU/day.
17407 *
17408 * <li> The proper motions are the rate of change of the right ascension
17409 * and declination at the catalog epoch and are in radians per Julian
17410 * year. The RA proper motion is in terms of coordinate angle, not
17411 * true angle, and will thus be numerically larger at high
17412 * declinations.
17413 *
17414 * <li> Straight-line motion at constant speed in the inertial frame is
17415 * assumed. If the speed is greater than or equal to the speed of
17416 * light, the function aborts with an error status.
17417 *
17418 * <li> The inverse transformation is performed by the function jauStarpv.
17419 *</ol>
17420 *<p>Called:<ul>
17421 * <li>{@link #jauPn} decompose p-vector into modulus and direction
17422 * <li>{@link #jauPdp} scalar product of two p-vectors
17423 * <li>{@link #jauSxp} multiply p-vector by scalar
17424 * <li>{@link #jauPmp} p-vector minus p-vector
17425 * <li>{@link #jauPm} modulus of p-vector
17426 * <li>{@link #jauPpp} p-vector plus p-vector
17427 * <li>{@link #jauPv2s} pv-vector to spherical
17428 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
17429 * </ul>
17430 *<p>Reference:
17431 *
17432 * Stumpff, P., 1985, Astron.Astrophys. 144, 232-240.
17433 *
17434 *@version 2008 May 18
17435 *
17436 * @since Release 20101201
17437 *
17438 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17439 */
17440 public static CatalogCoords jauPvstar(double pv[][]) throws JSOFAInternalError
17441 {
17442 double x[] = new double[3], vr, ur[] = new double[3], vt, ut[] = new double[3], bett, betr, d, w, del,
17443 usr[] = new double[3], ust[] = new double[3];
17444
17445
17446 /* Isolate the radial component of the velocity (AU/day, inertial). */
17447 NormalizedVector nv = jauPn(pv[0]);
17448 x = nv.u;
17449 vr = jauPdp(x, pv[1]);
17450 ur = jauSxp(vr,x);
17451
17452 /* Isolate the transverse component of the velocity (AU/day, inertial). */
17453 ut = jauPmp(pv[1], ur);
17454 vt = jauPm(ut);
17455
17456 /* Special-relativity dimensionless parameters. */
17457 bett = vt / DC;
17458 betr = vr / DC;
17459
17460 /* The inertial-to-observed correction terms. */
17461 d = 1.0 + betr;
17462 w = 1.0 - betr*betr - bett*bett;
17463 if (d == 0.0 || w < 0) throw new JSOFAInternalError("Superluminal speed", -1);
17464 del = sqrt(w) - 1.0;
17465
17466 /* Apply relativistic correction factor to radial velocity component. */
17467 w = (betr != 0) ? (betr - del) / (betr * d) : 1.0;
17468 usr = jauSxp(w,ur);
17469
17470 /* Apply relativistic correction factor to tangential velocity */
17471 /* component. */
17472 ust = jauSxp(1.0/d, ut);
17473
17474 /* Combine the two to obtain the observed velocity vector (AU/day). */
17475 pv[1] = jauPpp(usr, ust);
17476
17477 /* Cartesian to spherical. */
17478 SphericalPositionVelocity pvs = jauPv2s(pv);
17479 if (pvs.pos.r == 0.0) throw new JSOFAInternalError("null position vector", -2);
17480
17481 /* Return RA in range 0 to 2pi. */
17482 double ra = jauAnp(pvs.pos.theta);
17483
17484 /* Return proper motions in radians per year. */
17485 double pmr = pvs.vel.theta * DJY;
17486 double pmd = pvs.vel.phi * DJY;
17487
17488 /* Return parallax in arcsec. */
17489 double px = DR2AS / pvs.pos.r;
17490
17491 /* Return radial velocity in km/s. */
17492 double rv = 1e-3 * pvs.vel.r * DAU / DAYSEC;
17493
17494 /* OK status. */
17495 return new CatalogCoords(ra, pvs.pos.phi, pmr, pmd, px, rv);
17496
17497 }
17498
17499
17500 /**
17501 * Update a pv-vector.
17502 *
17503 *<p>This function is derived from the International Astronomical Union's
17504 * SOFA (Standards Of Fundamental Astronomy) software collection.
17505 *
17506 *<p>Status: vector/matrix support function.
17507 *
17508 *<!-- Given: -->
17509 * @param dt double time interval
17510 * @param pv double[2][3] pv-vector
17511 *
17512 *<!-- Returned: -->
17513 * @return upv double[2][3] <u>returned</u> p updated, v unchanged
17514 *
17515 * <p>Notes:
17516 * <ol>
17517 *
17518 * <li> "Update" means "refer the position component of the vector
17519 * to a new date dt time units from the existing date".
17520 *
17521 * <li> The time units of dt must match those of the velocity.
17522 *
17523 * <li> It is permissible for pv and upv to be the same array.
17524 *</ol>
17525 *<p>Called:<ul>
17526 * <li>{@link #jauPpsp} p-vector plus scaled p-vector
17527 * <li>{@link #jauCp} copy p-vector
17528 * </ul>
17529 *@version 2008 November 17
17530 *
17531 * @since Release 20101201
17532 *
17533 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17534 */
17535 public static double[][] jauPvu(double dt, double pv[][] )
17536 {
17537 double upv[][] = new double[2][3];
17538 upv[0] = jauPpsp(pv[0], dt, pv[1]);
17539 jauCp(pv[1], upv[1]);
17540
17541 return upv;
17542
17543 }
17544
17545
17546 /**
17547 * Update a pv-vector, discarding the velocity component.
17548 *
17549 *<p>This function is derived from the International Astronomical Union's
17550 * SOFA (Standards Of Fundamental Astronomy) software collection.
17551 *
17552 *<p>Status: vector/matrix support function.
17553 *
17554 *<!-- Given: -->
17555 * @param dt double time interval
17556 * @param pv double[2][3] pv-vector
17557 *
17558 *<!-- Returned: -->
17559 * @return p double[3] <u>returned</u> p-vector
17560 *
17561 * <p>Notes:
17562 * <ol>
17563 *
17564 * <li> "Update" means "refer the position component of the vector to a
17565 * new date dt time units from the existing date".
17566 *
17567 * <li> The time units of dt must match those of the velocity.
17568 *</ol>
17569 *@version 2008 May 11
17570 *
17571 * @since Release 20101201
17572 *
17573 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17574 */
17575 public static double[] jauPvup(double dt, double pv[][] )
17576 {
17577 double p[] = new double[3];
17578 p[0] = pv[0][0] + dt * pv[1][0];
17579 p[1] = pv[0][1] + dt * pv[1][1];
17580 p[2] = pv[0][2] + dt * pv[1][2];
17581
17582 return p;
17583
17584 }
17585
17586
17587 /**
17588 * Outer (=vector=cross) product of two pv-vectors.
17589 *
17590 *<p>This function is derived from the International Astronomical Union's
17591 * SOFA (Standards Of Fundamental Astronomy) software collection.
17592 *
17593 *<p>Status: vector/matrix support function.
17594 *
17595 *<!-- Given: -->
17596 * @param a double[2][3] first pv-vector
17597 * @param b double[2][3] second pv-vector
17598 *
17599 *<!-- Returned: -->
17600 * @return axb double[2][3] <u>returned</u> a x b
17601 *
17602 * <p>Notes:
17603 * <ol>
17604 *
17605 * <li> If the position and velocity components of the two pv-vectors are
17606 * ( ap, av ) and ( bp, bv ), the result, a x b, is the pair of
17607 * vectors ( ap x bp, ap x bv + av x bp ). The two vectors are the
17608 * cross-product of the two p-vectors and its derivative.
17609 *
17610 * <li> It is permissible to re-use the same array for any of the
17611 * arguments.
17612 *</ol>
17613 *<p>Called:<ul>
17614 * <li>{@link #jauCpv} copy pv-vector
17615 * <li>{@link #jauPxp} vector product of two p-vectors
17616 * <li>{@link #jauPpp} p-vector plus p-vector
17617 * </ul>
17618 *@version 2008 November 18
17619 *
17620 * @since Release 20101201
17621 *
17622 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17623 */
17624 public static double[][] jauPvxpv(double a[][], double b[][] )
17625 {
17626 double wa[][] = new double[2][3], wb[][] = new double[2][3], axbd[] = new double[3], adxb[] = new double[3];
17627
17628 double axb[][] = new double[2][3];
17629 /* Make copies of the inputs. */
17630 jauCpv(a, wa);
17631 jauCpv(b, wb);
17632
17633 /* a x b = position part of result. */
17634 axb[0] = jauPxp(wa[0], wb[0]);
17635
17636 /* a x bdot + adot x b = velocity part of result. */
17637 axbd = jauPxp(wa[0],wb[1]);
17638 adxb = jauPxp(wa[1],wb[0]);
17639 axb[1] = jauPpp(axbd, adxb);
17640
17641 return axb;
17642
17643 }
17644
17645
17646 /**
17647 * p-vector outer (=vector=cross) product.
17648 *
17649 *<p>This function is derived from the International Astronomical Union's
17650 * SOFA (Standards Of Fundamental Astronomy) software collection.
17651 *
17652 *<p>Status: vector/matrix support function.
17653 *
17654 *<!-- Given: -->
17655 * @param a double[3] first p-vector
17656 * @param b double[3] second p-vector
17657 *
17658 *<!-- Returned: -->
17659 * @return axb double[3] <u>returned</u> a x b
17660 *
17661 * Note:
17662 * It is permissible to re-use the same array for any of the
17663 * arguments.
17664 *
17665 *@version 2008 November 18
17666 *
17667 * @since Release 20101201
17668 *
17669 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17670 */
17671 public static double[] jauPxp(double a[] , double b[] )
17672 {
17673 double xa, ya, za, xb, yb, zb;
17674 double axb[] = new double[3];
17675
17676 xa = a[0];
17677 ya = a[1];
17678 za = a[2];
17679 xb = b[0];
17680 yb = b[1];
17681 zb = b[2];
17682 axb[0] = ya*zb - za*yb;
17683 axb[1] = za*xb - xa*zb;
17684 axb[2] = xa*yb - ya*xb;
17685
17686 return axb;
17687
17688 }
17689
17690
17691 /**
17692 * Express an r-matrix as an r-vector.
17693 *
17694 *<p>This function is derived from the International Astronomical Union's
17695 * SOFA (Standards Of Fundamental Astronomy) software collection.
17696 *
17697 *<p>Status: vector/matrix support function.
17698 *
17699 *<!-- Given: -->
17700 * @param r double[3][3] rotation matrix
17701 *
17702 *<!-- Returned: -->
17703 * @return w double[3] <u>returned</u> rotation vector (Note 1)
17704 *
17705 * <p>Notes:
17706 * <ol>
17707 *
17708 * <li> A rotation matrix describes a rotation through some angle about
17709 * some arbitrary axis called the Euler axis. The "rotation vector"
17710 * returned by this function has the same direction as the Euler axis,
17711 * and its magnitude is the angle in radians. (The magnitude and
17712 * direction can be separated by means of the function jauPn.)
17713 *
17714 * <li> If r is null, so is the result. If r is not a rotation matrix
17715 * the result is undefined; r must be proper (i.e. have a positive
17716 * determinant) and real orthogonal (inverse = transpose).
17717 *
17718 * <li> The reference frame rotates clockwise as seen looking along
17719 * the rotation vector from the origin.
17720 *</ol>
17721 *@version 2008 May 12
17722 *
17723 * @since Release 20101201
17724 *
17725 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17726 */
17727 public static double[] jauRm2v(double r[][] )
17728 {
17729 double x, y, z, s2, c2, phi, f;
17730 double w[] = new double[3];
17731
17732 x = r[1][2] - r[2][1];
17733 y = r[2][0] - r[0][2];
17734 z = r[0][1] - r[1][0];
17735 s2 = sqrt(x*x + y*y + z*z);
17736 if (s2 > 0) {
17737 c2 = r[0][0] + r[1][1] + r[2][2] - 1;
17738 phi = atan2(s2, c2);
17739 f = phi / s2;
17740 w[0] = x * f;
17741 w[1] = y * f;
17742 w[2] = z * f;
17743 } else {
17744 w[0] = 0.0;
17745 w[1] = 0.0;
17746 w[2] = 0.0;
17747 }
17748
17749 return w;
17750
17751 }
17752
17753
17754 /**
17755 * Form the r-matrix corresponding to a given r-vector.
17756 *
17757 *<p>This function is derived from the International Astronomical Union's
17758 * SOFA (Standards Of Fundamental Astronomy) software collection.
17759 *
17760 *<p>Status: vector/matrix support function.
17761 *
17762 *<!-- Given: -->
17763 * @param w double[3] rotation vector (Note 1)
17764 *
17765 *<!-- Returned: -->
17766 * @return r double[3][3] <u>returned</u> rotation matrix
17767 *
17768 * <p>Notes:
17769 * <ol>
17770 *
17771 * <li> A rotation matrix describes a rotation through some angle about
17772 * some arbitrary axis called the Euler axis. The "rotation vector"
17773 * supplied to This function has the same direction as the Euler
17774 * axis, and its magnitude is the angle in radians.
17775 *
17776 * <li> If w is null, the unit matrix is returned.
17777 *
17778 * <li> The reference frame rotates clockwise as seen looking along the
17779 * rotation vector from the origin.
17780 *</ol>
17781 *@version 2008 May 11
17782 *
17783 * @since Release 20101201
17784 *
17785 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17786 */
17787 public static double[][] jauRv2m(double w[])
17788 {
17789 double x, y, z, phi, s, c, f;
17790 double r[][] = new double[3][3];
17791
17792
17793 /* Euler angle (magnitude of rotation vector) and functions. */
17794 x = w[0];
17795 y = w[1];
17796 z = w[2];
17797 phi = sqrt(x*x + y*y + z*z);
17798 s = sin(phi);
17799 c = cos(phi);
17800 f = 1.0 - c;
17801
17802 /* Euler axis (direction of rotation vector), perhaps null. */
17803 if (phi > 0.0) {
17804 x /= phi;
17805 y /= phi;
17806 z /= phi;
17807 }
17808
17809 /* Form the rotation matrix. */
17810 r[0][0] = x*x*f + c;
17811 r[0][1] = x*y*f + z*s;
17812 r[0][2] = x*z*f - y*s;
17813 r[1][0] = y*x*f - z*s;
17814 r[1][1] = y*y*f + c;
17815 r[1][2] = y*z*f + x*s;
17816 r[2][0] = z*x*f + y*s;
17817 r[2][1] = z*y*f - x*s;
17818 r[2][2] = z*z*f + c;
17819
17820 return r;
17821
17822 }
17823
17824
17825 /**
17826 * Rotate an r-matrix about the x-axis.
17827 *
17828 *<p>This function is derived from the International Astronomical Union's
17829 * SOFA (Standards Of Fundamental Astronomy) software collection.
17830 *
17831 *<p>Status: vector/matrix support function.
17832 *
17833 *<!-- Given: -->
17834 * @param phi double angle (radians)
17835 *
17836 * Given and returned:
17837 * @param r double[3][3] r-matrix <u>given and returned</u>
17838 *
17839 * Sign convention: The matrix can be used to rotate the reference
17840 * frame of a vector. Calling this function with positive phi
17841 * incorporates in the matrix an additional rotation, about the x-axis,
17842 * anticlockwise as seen looking towards the origin from positive x.
17843 *
17844 *<p>Called:<ul>
17845 * <li>{@link #jauIr} initialize r-matrix to identity
17846 * <li>{@link #jauRxr} product of two r-matrices
17847 * <li>{@link #jauCr} copy r-matrix
17848 * </ul>
17849 *@version 2008 May 22
17850 *
17851 * @since Release 20101201
17852 *
17853 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17854 */
17855 public static void jauRx(double phi, double r[][])
17856 {
17857 double s, c, a[][] = new double[3][3], w[][];
17858
17859
17860 /* Matrix representing new rotation. */
17861 s = sin(phi);
17862 c = cos(phi);
17863 jauIr(a);
17864 a[1][1] = c;
17865 a[2][1] = -s;
17866 a[1][2] = s;
17867 a[2][2] = c;
17868
17869 /* Rotate. */
17870 w = jauRxr(a, r);
17871
17872 /* Return result. */
17873 jauCr(w, r);
17874
17875 return;
17876
17877 }
17878
17879
17880 /**
17881 * Multiply a p-vector by an r-matrix.
17882 *
17883 *<p>This function is derived from the International Astronomical Union's
17884 * SOFA (Standards Of Fundamental Astronomy) software collection.
17885 *
17886 *<p>Status: vector/matrix support function.
17887 *
17888 *<!-- Given: -->
17889 * @param r double[3][3] r-matrix
17890 * @param p double[3] p-vector
17891 *
17892 *<!-- Returned: -->
17893 * @return rp double[3] <u>returned</u> r * p
17894 *
17895 * Note:
17896 * It is permissible for p and rp to be the same array.
17897 *
17898 *<p>Called:<ul>
17899 * <li>{@link #jauCp} copy p-vector
17900 * </ul>
17901 *@version 2008 October 28
17902 *
17903 * @since Release 20101201
17904 *
17905 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17906 */
17907 public static double[] jauRxp(double r[][], double p[])
17908 {
17909 double w, wrp[] = new double[3] ;
17910 int i, j;
17911
17912
17913 /* Matrix r * vector p. */
17914 for (j = 0; j < 3; j++) {
17915 w = 0.0;
17916 for (i = 0; i < 3; i++) {
17917 w += r[j][i] * p[i];
17918 }
17919 wrp[j] = w;
17920 }
17921
17922
17923 return wrp;
17924
17925 }
17926
17927
17928 /**
17929 * Multiply a pv-vector by an r-matrix.
17930 *
17931 *<p>This function is derived from the International Astronomical Union's
17932 * SOFA (Standards Of Fundamental Astronomy) software collection.
17933 *
17934 *<p>Status: vector/matrix support function.
17935 *
17936 *<!-- Given: -->
17937 * @param r double[3][3] r-matrix
17938 * @param pv double[2][3] pv-vector
17939 *
17940 *<!-- Returned: -->
17941 * @return rpv double[2][3] <u>returned</u> r * pv
17942 *
17943 * Note:
17944 * It is permissible for pv and rpv to be the same array.
17945 *
17946 *<p>Called:<ul>
17947 * <li>{@link #jauRxp} product of r-matrix and p-vector
17948 * </ul>
17949 *@version 2008 October 28
17950 *
17951 * @since Release 20101201
17952 *
17953 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17954 */
17955 public static double[][] jauRxpv(double r[][], double pv[][])
17956 {
17957 double rpv[][] = new double[2][0];
17958 rpv[0] = jauRxp(r, pv[0]);
17959 rpv[1] = jauRxp(r, pv[1]);
17960
17961 return rpv;
17962
17963 }
17964
17965
17966 /**
17967 * Multiply two r-matrices.
17968 *
17969 *<p>This function is derived from the International Astronomical Union's
17970 * SOFA (Standards Of Fundamental Astronomy) software collection.
17971 *
17972 *<p>Status: vector/matrix support function.
17973 *
17974 *<!-- Given: -->
17975 * @param a double[3][3] first r-matrix
17976 * @param b double[3][3] second r-matrix
17977 *
17978 *<!-- Returned: -->
17979 * @return atb double[3][3] <u>returned</u> a * b
17980 *
17981 * Note:
17982 * It is permissible to re-use the same array for any of the
17983 * arguments.
17984 *
17985 *<p>Called:<ul>
17986 * <li>{@link #jauCr} copy r-matrix
17987 * </ul>
17988 *@version 2008 November 18
17989 *
17990 * @since Release 20101201
17991 *
17992 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17993 */
17994 public static double[][] jauRxr(double a[][], double b[][])
17995 {
17996 int i, j, k;
17997 double w, wm[][] = new double[3][3];
17998
17999
18000 for (i = 0; i < 3; i++) {
18001 for (j = 0; j < 3; j++) {
18002 w = 0.0;
18003 for (k = 0; k < 3; k++) {
18004 w += a[i][k] * b[k][j];
18005 }
18006 wm[i][j] = w;
18007 }
18008 }
18009
18010 return wm;
18011
18012 }
18013
18014
18015 /**
18016 * Rotate an r-matrix about the y-axis.
18017 *
18018 *<p>This function is derived from the International Astronomical Union's
18019 * SOFA (Standards Of Fundamental Astronomy) software collection.
18020 *
18021 *<p>Status: vector/matrix support function.
18022 *
18023 *<!-- Given: -->
18024 * @param theta double angle (radians)
18025 *
18026 * Given and returned:
18027 * @param r double[3][3] <u>given & returned</u> r-matrix
18028 *
18029 * Sign convention: The matrix can be used to rotate the reference
18030 * frame of a vector. Calling This function with positive theta
18031 * incorporates in the matrix an additional rotation, about the y-axis,
18032 * anticlockwise as seen looking towards the origin from positive y.
18033 *
18034 *<p>Called:<ul>
18035 * <li>{@link #jauIr} initialize r-matrix to identity
18036 * <li>{@link #jauRxr} product of two r-matrices
18037 * <li>{@link #jauCr} copy r-matrix
18038 * </ul>
18039 *@version 2008 May 22
18040 *
18041 * @since Release 20101201
18042 *
18043 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
18044 */
18045 public static void jauRy(double theta, double r[][])
18046 {
18047 double s, c, a[][] = new double[3][3], w[][];
18048
18049
18050 /* Matrix representing new rotation. */
18051 s = sin(theta);
18052 c = cos(theta);
18053 jauIr(a);
18054 a[0][0] = c;
18055 a[2][0] = s;
18056 a[0][2] = -s;
18057 a[2][2] = c;
18058
18059 /* Rotate. */
18060 w = jauRxr(a, r);
18061
18062 /* Return result. */
18063 jauCr(w, r);
18064
18065 return;
18066
18067 }
18068
18069
18070 /**
18071 * Rotate an r-matrix about the z-axis.
18072 *
18073 *<p>This function is derived from the International Astronomical Union's
18074 * SOFA (Standards Of Fundamental Astronomy) software collection.
18075 *
18076 *<p>Status: vector/matrix support function.
18077 *
18078 *<!-- Given: -->
18079 * @param psi double angle (radians)
18080 *
18081 * Given and returned:
18082 * @param r double[3][3] <u>given & retuned</u>r-matrix, rotated
18083 *
18084 * Sign convention: The matrix can be used to rotate the reference
18085 * frame of a vector. Calling This function with positive psi
18086 * incorporates in the matrix an additional rotation, about the z-axis,
18087 * anticlockwise as seen looking towards the origin from positive z.
18088 *
18089 *<p>Called:<ul>
18090 * <li>{@link #jauIr} initialize r-matrix to identity
18091 * <li>{@link #jauRxr} product of two r-matrices
18092 * <li>{@link #jauCr} copy r-matrix
18093 * </ul>
18094 *@version 2008 May 22
18095 *
18096 * @since Release 20101201
18097 *
18098 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
18099 */
18100 public static void jauRz(double psi, double r[][])
18101 {
18102 double s, c, a[][] = new double[3][3], w[][];
18103
18104
18105 /* Matrix representing new rotation. */
18106 s = sin(psi);
18107 c = cos(psi);
18108 jauIr(a);
18109 a[0][0] = c;
18110 a[1][0] = -s;
18111 a[0][1] = s;
18112 a[1][1] = c;
18113
18114 /* Rotate. */
18115 w = jauRxr(a, r);
18116
18117 /* Return result. */
18118 jauCr(w, r);
18119
18120 return;
18121
18122 }
18123
18124
18125 /**
18126 * The CIO locator s, positioning the Celestial Intermediate Origin on
18127 * the equator of the Celestial Intermediate Pole, given the CIP's X,Y
18128 * coordinates. Compatible with IAU 2000A precession-nutation.
18129 *
18130 *<p>This function is derived from the International Astronomical Union's
18131 * SOFA (Standards Of Fundamental Astronomy) software collection.
18132 *
18133 *<p>Status: canonical model.
18134 *
18135 *<!-- Given: -->
18136 * @param date1 double TT as a 2-part Julian Date (Note 1)
18137 * @param date2 double TT as a 2-part Julian Date (Note 1)
18138 * @param x double CIP coordinates (Note 3)
18139 * @param y double CIP coordinates (Note 3)
18140 *
18141 * <!-- Returned (function value): -->
18142 * @return double the CIO locator s in radians (Note 2)
18143 *
18144 * <p>Notes:
18145 * <ol>
18146 *
18147 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
18148 * convenient way between the two arguments. For example,
18149 * JD(TT)=2450123.7 could be expressed in any of these ways,
18150 * among others:
18151 *<pre>
18152 * date1 date2
18153 *
18154 * 2450123.7 0.0 (JD method)
18155 * 2451545.0 -1421.3 (J2000 method)
18156 * 2400000.5 50123.2 (MJD method)
18157 * 2450123.5 0.2 (date & time method)
18158 *</pre>
18159 * The JD method is the most natural and convenient to use in
18160 * cases where the loss of several decimal digits of resolution
18161 * is acceptable. The J2000 method is best matched to the way
18162 * the argument is handled internally and will deliver the
18163 * optimum resolution. The MJD method and the date & time methods
18164 * are both good compromises between resolution and convenience.
18165 *
18166 * <li> The CIO locator s is the difference between the right ascensions
18167 * of the same point in two systems: the two systems are the GCRS
18168 * and the CIP,CIO, and the point is the ascending node of the
18169 * CIP equator. The quantity s remains below 0.1 arcsecond
18170 * throughout 1900-2100.
18171 *
18172 * <li> The series used to compute s is in fact for s+XY/2, where X and Y
18173 * are the x and y components of the CIP unit vector; this series
18174 * is more compact than a direct series for s would be. This
18175 * function requires X,Y to be supplied by the caller, who is
18176 * responsible for providing values that are consistent with the
18177 * supplied date.
18178 *
18179 * <li> The model is consistent with the IAU 2000A precession-nutation.
18180 *</ol>
18181 *<p>Called:<ul>
18182 * <li>{@link #jauFal03} mean anomaly of the Moon
18183 * <li>{@link #jauFalp03} mean anomaly of the Sun
18184 * <li>{@link #jauFaf03} mean argument of the latitude of the Moon
18185 * <li>{@link #jauFad03} mean elongation of the Moon from the Sun
18186 * <li>{@link #jauFaom03} mean longitude of the Moon's ascending node
18187 * <li>{@link #jauFave03} mean longitude of Venus
18188 * <li>{@link #jauFae03} mean longitude of Earth
18189 * <li>{@link #jauFapa03} general accumulated precession in longitude
18190 * </ul>
18191 *<p>References:
18192 *
18193 * <p>Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
18194 * "Expressions for the Celestial Intermediate Pole and Celestial
18195 * Ephemeris Origin consistent with the IAU 2000A precession-
18196 * nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
18197 *
18198 * n.b. The celestial ephemeris origin (CEO) was renamed "celestial
18199 * intermediate origin" (CIO) by IAU 2006 Resolution 2.
18200 *
18201 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
18202 * IERS Technical Note No. 32, BKG (2004)
18203 *
18204 *@version 2010 January 18
18205 *
18206 * @since Release 20101201
18207 *
18208 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
18209 */
18210 public static double jauS00(double date1, double date2, double x, double y)
18211 {
18212 /* Time since J2000.0, in Julian centuries */
18213 double t;
18214
18215 /* Miscellaneous */
18216 int i, j;
18217 double a, w0, w1, w2, w3, w4, w5;
18218
18219 /* Fundamental arguments */
18220 double fa[] = new double[8];
18221
18222 /* Returned value */
18223 double s;
18224
18225 /* --------------------- */
18226 /* The series for s+XY/2 */
18227 /* --------------------- */
18228
18229 /* Polynomial coefficients */
18230 final double sp[] = {
18231
18232 /* 1-6 */
18233 94.00e-6,
18234 3808.35e-6,
18235 -119.94e-6,
18236 -72574.09e-6,
18237 27.70e-6,
18238 15.61e-6
18239 };
18240
18241 /* Terms of order t^0 */
18242 final TERM s0[] = {
18243
18244 /* 1-10 */
18245 new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, -2640.73e-6, 0.39e-6 ),
18246 new TERM(new int[]{ 0, 0, 0, 0, 2, 0, 0, 0}, -63.53e-6, 0.02e-6 ),
18247 new TERM(new int[]{ 0, 0, 2, -2, 3, 0, 0, 0}, -11.75e-6, -0.01e-6 ),
18248 new TERM(new int[]{ 0, 0, 2, -2, 1, 0, 0, 0}, -11.21e-6, -0.01e-6 ),
18249 new TERM(new int[]{ 0, 0, 2, -2, 2, 0, 0, 0}, 4.57e-6, 0.00e-6 ),
18250 new TERM(new int[]{ 0, 0, 2, 0, 3, 0, 0, 0}, -2.02e-6, 0.00e-6 ),
18251 new TERM(new int[]{ 0, 0, 2, 0, 1, 0, 0, 0}, -1.98e-6, 0.00e-6 ),
18252 new TERM(new int[]{ 0, 0, 0, 0, 3, 0, 0, 0}, 1.72e-6, 0.00e-6 ),
18253 new TERM(new int[]{ 0, 1, 0, 0, 1, 0, 0, 0}, 1.41e-6, 0.01e-6 ),
18254 new TERM(new int[]{ 0, 1, 0, 0, -1, 0, 0, 0}, 1.26e-6, 0.01e-6 ),
18255
18256 /* 11-20 */
18257 new TERM(new int[]{ 1, 0, 0, 0, -1, 0, 0, 0}, 0.63e-6, 0.00e-6 ),
18258 new TERM(new int[]{ 1, 0, 0, 0, 1, 0, 0, 0}, 0.63e-6, 0.00e-6 ),
18259 new TERM(new int[]{ 0, 1, 2, -2, 3, 0, 0, 0}, -0.46e-6, 0.00e-6 ),
18260 new TERM(new int[]{ 0, 1, 2, -2, 1, 0, 0, 0}, -0.45e-6, 0.00e-6 ),
18261 new TERM(new int[]{ 0, 0, 4, -4, 4, 0, 0, 0}, -0.36e-6, 0.00e-6 ),
18262 new TERM(new int[]{ 0, 0, 1, -1, 1, -8, 12, 0}, 0.24e-6, 0.12e-6 ),
18263 new TERM(new int[]{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.32e-6, 0.00e-6 ),
18264 new TERM(new int[]{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.28e-6, 0.00e-6 ),
18265 new TERM(new int[]{ 1, 0, 2, 0, 3, 0, 0, 0}, -0.27e-6, 0.00e-6 ),
18266 new TERM(new int[]{ 1, 0, 2, 0, 1, 0, 0, 0}, -0.26e-6, 0.00e-6 ),
18267
18268 /* 21-30 */
18269 new TERM(new int[]{ 0, 0, 2, -2, 0, 0, 0, 0}, 0.21e-6, 0.00e-6 ),
18270 new TERM(new int[]{ 0, 1, -2, 2, -3, 0, 0, 0}, -0.19e-6, 0.00e-6 ),
18271 new TERM(new int[]{ 0, 1, -2, 2, -1, 0, 0, 0}, -0.18e-6, 0.00e-6 ),
18272 new TERM(new int[]{ 0, 0, 0, 0, 0, 8,-13, -1}, 0.10e-6, -0.05e-6 ),
18273 new TERM(new int[]{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.15e-6, 0.00e-6 ),
18274 new TERM(new int[]{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.14e-6, 0.00e-6 ),
18275 new TERM(new int[]{ 0, 1, 2, -2, 2, 0, 0, 0}, 0.14e-6, 0.00e-6 ),
18276 new TERM(new int[]{ 1, 0, 0, -2, 1, 0, 0, 0}, -0.14e-6, 0.00e-6 ),
18277 new TERM(new int[]{ 1, 0, 0, -2, -1, 0, 0, 0}, -0.14e-6, 0.00e-6 ),
18278 new TERM(new int[]{ 0, 0, 4, -2, 4, 0, 0, 0}, -0.13e-6, 0.00e-6 ),
18279
18280 /* 31-33 */
18281 new TERM(new int[]{ 0, 0, 2, -2, 4, 0, 0, 0}, 0.11e-6, 0.00e-6 ),
18282 new TERM(new int[]{ 1, 0, -2, 0, -3, 0, 0, 0}, -0.11e-6, 0.00e-6 ),
18283 new TERM(new int[]{ 1, 0, -2, 0, -1, 0, 0, 0}, -0.11e-6, 0.00e-6 )
18284 };
18285
18286 /* Terms of order t^1 */
18287 final TERM s1[] ={
18288
18289 /* 1-3 */
18290 new TERM(new int[]{ 0, 0, 0, 0, 2, 0, 0, 0}, -0.07e-6, 3.57e-6 ),
18291 new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, 1.71e-6, -0.03e-6 ),
18292 new TERM(new int[]{ 0, 0, 2, -2, 3, 0, 0, 0}, 0.00e-6, 0.48e-6 )
18293 };
18294
18295 /* Terms of order t^2 */
18296 final TERM s2[] ={
18297
18298 /* 1-10 */
18299 new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, 743.53e-6, -0.17e-6 ),
18300 new TERM(new int[]{ 0, 0, 2, -2, 2, 0, 0, 0}, 56.91e-6, 0.06e-6 ),
18301 new TERM(new int[]{ 0, 0, 2, 0, 2, 0, 0, 0}, 9.84e-6, -0.01e-6 ),
18302 new TERM(new int[]{ 0, 0, 0, 0, 2, 0, 0, 0}, -8.85e-6, 0.01e-6 ),
18303 new TERM(new int[]{ 0, 1, 0, 0, 0, 0, 0, 0}, -6.38e-6, -0.05e-6 ),
18304 new TERM(new int[]{ 1, 0, 0, 0, 0, 0, 0, 0}, -3.07e-6, 0.00e-6 ),
18305 new TERM(new int[]{ 0, 1, 2, -2, 2, 0, 0, 0}, 2.23e-6, 0.00e-6 ),
18306 new TERM(new int[]{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.67e-6, 0.00e-6 ),
18307 new TERM(new int[]{ 1, 0, 2, 0, 2, 0, 0, 0}, 1.30e-6, 0.00e-6 ),
18308 new TERM(new int[]{ 0, 1, -2, 2, -2, 0, 0, 0}, 0.93e-6, 0.00e-6 ),
18309
18310 /* 11-20 */
18311 new TERM(new int[]{ 1, 0, 0, -2, 0, 0, 0, 0}, 0.68e-6, 0.00e-6 ),
18312 new TERM(new int[]{ 0, 0, 2, -2, 1, 0, 0, 0}, -0.55e-6, 0.00e-6 ),
18313 new TERM(new int[]{ 1, 0, -2, 0, -2, 0, 0, 0}, 0.53e-6, 0.00e-6 ),
18314 new TERM(new int[]{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.27e-6, 0.00e-6 ),
18315 new TERM(new int[]{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.27e-6, 0.00e-6 ),
18316 new TERM(new int[]{ 1, 0, -2, -2, -2, 0, 0, 0}, -0.26e-6, 0.00e-6 ),
18317 new TERM(new int[]{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.25e-6, 0.00e-6 ),
18318 new TERM(new int[]{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.22e-6, 0.00e-6 ),
18319 new TERM(new int[]{ 2, 0, 0, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 ),
18320 new TERM(new int[]{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.20e-6, 0.00e-6 ),
18321
18322 /* 21-25 */
18323 new TERM(new int[]{ 0, 0, 2, 2, 2, 0, 0, 0}, 0.17e-6, 0.00e-6 ),
18324 new TERM(new int[]{ 2, 0, 2, 0, 2, 0, 0, 0}, 0.13e-6, 0.00e-6 ),
18325 new TERM(new int[]{ 2, 0, 0, 0, 0, 0, 0, 0}, -0.13e-6, 0.00e-6 ),
18326 new TERM(new int[]{ 1, 0, 2, -2, 2, 0, 0, 0}, -0.12e-6, 0.00e-6 ),
18327 new TERM(new int[]{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.11e-6, 0.00e-6 )
18328 };
18329
18330 /* Terms of order t^3 */
18331 final TERM s3[] ={
18332
18333 /* 1-4 */
18334 new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, 0.30e-6, -23.51e-6 ),
18335 new TERM(new int[]{ 0, 0, 2, -2, 2, 0, 0, 0}, -0.03e-6, -1.39e-6 ),
18336 new TERM(new int[]{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.01e-6, -0.24e-6 ),
18337 new TERM(new int[]{ 0, 0, 0, 0, 2, 0, 0, 0}, 0.00e-6, 0.22e-6 )
18338 };
18339
18340 /* Terms of order t^4 */
18341 final TERM s4[] ={
18342
18343 /* 1-1 */
18344 new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.26e-6, -0.01e-6 )
18345 };
18346
18347 /* Number of terms in the series */
18348 final int NS0 = s0.length;
18349 final int NS1 = s1.length;
18350 final int NS2 = s2.length;
18351 final int NS3 = s3.length;
18352 final int NS4 = s4.length;
18353
18354 /*--------------------------------------------------------------------*/
18355
18356 /* Interval between fundamental epoch J2000.0 and current date (JC). */
18357 t = ((date1 - DJ00) + date2) / DJC;
18358
18359 /* Fundamental Arguments (from IERS Conventions 2003) */
18360
18361 /* Mean anomaly of the Moon. */
18362 fa[0] = jauFal03(t);
18363
18364 /* Mean anomaly of the Sun. */
18365 fa[1] = jauFalp03(t);
18366
18367 /* Mean longitude of the Moon minus that of the ascending node. */
18368 fa[2] = jauFaf03(t);
18369
18370 /* Mean elongation of the Moon from the Sun. */
18371 fa[3] = jauFad03(t);
18372
18373 /* Mean longitude of the ascending node of the Moon. */
18374 fa[4] = jauFaom03(t);
18375
18376 /* Mean longitude of Venus. */
18377 fa[5] = jauFave03(t);
18378
18379 /* Mean longitude of Earth. */
18380 fa[6] = jauFae03(t);
18381
18382 /* General precession in longitude. */
18383 fa[7] = jauFapa03(t);
18384
18385 /* Evaluate s. */
18386 w0 = sp[0];
18387 w1 = sp[1];
18388 w2 = sp[2];
18389 w3 = sp[3];
18390 w4 = sp[4];
18391 w5 = sp[5];
18392
18393 for (i = NS0-1; i >= 0; i--) {
18394 a = 0.0;
18395 for (j = 0; j < 8; j++) {
18396 a += (double)s0[i].nfa[j] * fa[j];
18397 }
18398 w0 += s0[i].s * sin(a) + s0[i].c * cos(a);
18399 }
18400
18401 for (i = NS1-1; i >= 0; i--) {
18402 a = 0.0;
18403 for (j = 0; j < 8; j++) {
18404 a += (double)s1[i].nfa[j] * fa[j];
18405 }
18406 w1 += s1[i].s * sin(a) + s1[i].c * cos(a);
18407 }
18408
18409 for (i = NS2-1; i >= 0; i--) {
18410 a = 0.0;
18411 for (j = 0; j < 8; j++) {
18412 a += (double)s2[i].nfa[j] * fa[j];
18413 }
18414 w2 += s2[i].s * sin(a) + s2[i].c * cos(a);
18415 }
18416
18417 for (i = NS3-1; i >= 0; i--) {
18418 a = 0.0;
18419 for (j = 0; j < 8; j++) {
18420 a += (double)s3[i].nfa[j] * fa[j];
18421 }
18422 w3 += s3[i].s * sin(a) + s3[i].c * cos(a);
18423 }
18424
18425 for (i = NS4-1; i >= 0; i--) {
18426 a = 0.0;
18427 for (j = 0; j < 8; j++) {
18428 a += (double)s4[i].nfa[j] * fa[j];
18429 }
18430 w4 += s4[i].s * sin(a) + s4[i].c * cos(a);
18431 }
18432
18433 s = (w0 +
18434 (w1 +
18435 (w2 +
18436 (w3 +
18437 (w4 +
18438 w5 * t) * t) * t) * t) * t) * DAS2R - x*y/2.0;
18439
18440 return s;
18441
18442 }
18443
18444
18445 /**
18446 * The CIO locator s, positioning the Celestial Intermediate Origin on
18447 * the equator of the Celestial Intermediate Pole, using the IAU 2000A
18448 * precession-nutation model.
18449 *
18450 *<p>This function is derived from the International Astronomical Union's
18451 * SOFA (Standards Of Fundamental Astronomy) software collection.
18452 *
18453 *<p>Status: support function.
18454 *
18455 *<!-- Given: -->
18456 * @param date1 double TT as a 2-part Julian Date (Note 1)
18457 * @param date2 double TT as a 2-part Julian Date (Note 1)
18458 *
18459 * <!-- Returned (function value): -->
18460 * @return double the CIO locator s in radians (Note 2)
18461 *
18462 * <p>Notes:
18463 * <ol>
18464 *
18465 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
18466 * convenient way between the two arguments. For example,
18467 * JD(TT)=2450123.7 could be expressed in any of these ways,
18468 * among others:
18469 *<pre>
18470 * date1 date2
18471 *
18472 * 2450123.7 0.0 (JD method)
18473 * 2451545.0 -1421.3 (J2000 method)
18474 * 2400000.5 50123.2 (MJD method)
18475 * 2450123.5 0.2 (date & time method)
18476 *</pre>
18477 * The JD method is the most natural and convenient to use in
18478 * cases where the loss of several decimal digits of resolution
18479 * is acceptable. The J2000 method is best matched to the way
18480 * the argument is handled internally and will deliver the
18481 * optimum resolution. The MJD method and the date & time methods
18482 * are both good compromises between resolution and convenience.
18483 *
18484 * <li> The CIO locator s is the difference between the right ascensions
18485 * of the same point in two systems. The two systems are the GCRS
18486 * and the CIP,CIO, and the point is the ascending node of the
18487 * CIP equator. The CIO locator s remains a small fraction of
18488 * 1 arcsecond throughout 1900-2100.
18489 *
18490 * <li> The series used to compute s is in fact for s+XY/2, where X and Y
18491 * are the x and y components of the CIP unit vector; this series
18492 * is more compact than a direct series for s would be. The present
18493 * function uses the full IAU 2000A nutation model when predicting
18494 * the CIP position. Faster results, with no significant loss of
18495 * accuracy, can be obtained via the function jauS00b, which uses
18496 * instead the IAU 2000B truncated model.
18497 *</ol>
18498 *<p>Called:<ul>
18499 * <li>{@link #jauPnm00a} classical NPB matrix, IAU 2000A
18500 * <li>{@link #jauBpn2xy} extract CIP X,Y from the BPN matrix
18501 * <li>{@link #jauS00} the CIO locator s, given X,Y, IAU 2000A
18502 * </ul>
18503 *<p>References:
18504 *
18505 * <p>Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
18506 * "Expressions for the Celestial Intermediate Pole and Celestial
18507 * Ephemeris Origin consistent with the IAU 2000A precession-
18508 * nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
18509 *
18510 * n.b. The celestial ephemeris origin (CEO) was renamed "celestial
18511 * intermediate origin" (CIO) by IAU 2006 Resolution 2.
18512 *
18513 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
18514 * IERS Technical Note No. 32, BKG (2004)
18515 *
18516 *@version 2010 January 18
18517 *
18518 * @since Release 20101201
18519 *
18520 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
18521 */
18522 public static double jauS00a(double date1, double date2)
18523 {
18524 double s;
18525
18526
18527 /* Bias-precession-nutation-matrix, IAU 2000A. */
18528 double rbpn[][] = jauPnm00a(date1, date2);
18529
18530 /* Extract the CIP coordinates. */
18531 CelestialIntermediatePole cip = jauBpn2xy(rbpn);
18532
18533 /* Compute the CIO locator s, given the CIP coordinates. */
18534 s = jauS00(date1, date2, cip.x, cip.y);
18535
18536 return s;
18537
18538 }
18539
18540
18541 /**
18542 * The CIO locator s, positioning the Celestial Intermediate Origin on
18543 * the equator of the Celestial Intermediate Pole, using the IAU 2000B
18544 * precession-nutation model.
18545 *
18546 *<p>This function is derived from the International Astronomical Union's
18547 * SOFA (Standards Of Fundamental Astronomy) software collection.
18548 *
18549 *<p>Status: support function.
18550 *
18551 *<!-- Given: -->
18552 * @param date1 double TT as a 2-part Julian Date (Note 1)
18553 * @param date2 double TT as a 2-part Julian Date (Note 1)
18554 *
18555 * <!-- Returned (function value): -->
18556 * @return double the CIO locator s in radians (Note 2)
18557 *
18558 * <p>Notes:
18559 * <ol>
18560 *
18561 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
18562 * convenient way between the two arguments. For example,
18563 * JD(TT)=2450123.7 could be expressed in any of these ways,
18564 * among others:
18565 *<pre>
18566 * date1 date2
18567 *
18568 * 2450123.7 0.0 (JD method)
18569 * 2451545.0 -1421.3 (J2000 method)
18570 * 2400000.5 50123.2 (MJD method)
18571 * 2450123.5 0.2 (date & time method)
18572 *</pre>
18573 * The JD method is the most natural and convenient to use in
18574 * cases where the loss of several decimal digits of resolution
18575 * is acceptable. The J2000 method is best matched to the way
18576 * the argument is handled internally and will deliver the
18577 * optimum resolution. The MJD method and the date & time methods
18578 * are both good compromises between resolution and convenience.
18579 *
18580 * <li> The CIO locator s is the difference between the right ascensions
18581 * of the same point in two systems. The two systems are the GCRS
18582 * and the CIP,CIO, and the point is the ascending node of the
18583 * CIP equator. The CIO locator s remains a small fraction of
18584 * 1 arcsecond throughout 1900-2100.
18585 *
18586 * <li> The series used to compute s is in fact for s+XY/2, where X and Y
18587 * are the x and y components of the CIP unit vector; this series
18588 * is more compact than a direct series for s would be. The present
18589 * function uses the IAU 2000B truncated nutation model when
18590 * predicting the CIP position. The function jauS00a uses instead
18591 * the full IAU 2000A model, but with no significant increase in
18592 * accuracy and at some cost in speed.
18593 *</ol>
18594 *<p>Called:<ul>
18595 * <li>{@link #jauPnm00b} classical NPB matrix, IAU 2000B
18596 * <li>{@link #jauBpn2xy} extract CIP X,Y from the BPN matrix
18597 * <li>{@link #jauS00} the CIO locator s, given X,Y, IAU 2000A
18598 * </ul>
18599 *<p>References:
18600 *
18601 * <p>Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
18602 * "Expressions for the Celestial Intermediate Pole and Celestial
18603 * Ephemeris Origin consistent with the IAU 2000A precession-
18604 * nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
18605 *
18606 * n.b. The celestial ephemeris origin (CEO) was renamed "celestial
18607 * intermediate origin" (CIO) by IAU 2006 Resolution 2.
18608 *
18609 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
18610 * IERS Technical Note No. 32, BKG (2004)
18611 *
18612 *@version 2010 January 18
18613 *
18614 * @since Release 20101201
18615 *
18616 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
18617 */
18618 public static double jauS00b(double date1, double date2)
18619 {
18620 double rbpn[][] = new double[3][3], s;
18621
18622
18623 /* Bias-precession-nutation-matrix, IAU 2000B. */
18624 rbpn = jauPnm00b(date1, date2);
18625
18626 /* Extract the CIP coordinates. */
18627 CelestialIntermediatePole cip = jauBpn2xy(rbpn);
18628
18629 /* Compute the CIO locator s, given the CIP coordinates. */
18630 s = jauS00(date1, date2, cip.x, cip.y);
18631
18632 return s;
18633
18634 }
18635
18636
18637 /**
18638 * The CIO locator s, positioning the Celestial Intermediate Origin on
18639 * the equator of the Celestial Intermediate Pole, given the CIP's X,Y
18640 * coordinates. Compatible with IAU 2006/2000A precession-nutation.
18641 *
18642 *<p>This function is derived from the International Astronomical Union's
18643 * SOFA (Standards Of Fundamental Astronomy) software collection.
18644 *
18645 *<p>Status: canonical model.
18646 *
18647 *<!-- Given: -->
18648 * @param date1 double TT as a 2-part Julian Date (Note 1)
18649 * @param date2 double TT as a 2-part Julian Date (Note 1)
18650 * @param x double CIP coordinates (Note 3)
18651 * @param y double CIP coordinates (Note 3)
18652 *
18653 * <!-- Returned (function value): -->
18654 * @return double the CIO locator s in radians (Note 2)
18655 *
18656 * <p>Notes:
18657 * <ol>
18658 *
18659 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
18660 * convenient way between the two arguments. For example,
18661 * JD(TT)=2450123.7 could be expressed in any of these ways,
18662 * among others:
18663 *<pre>
18664 * date1 date2
18665 *
18666 * 2450123.7 0.0 (JD method)
18667 * 2451545.0 -1421.3 (J2000 method)
18668 * 2400000.5 50123.2 (MJD method)
18669 * 2450123.5 0.2 (date & time method)
18670 *</pre>
18671 * The JD method is the most natural and convenient to use in
18672 * cases where the loss of several decimal digits of resolution
18673 * is acceptable. The J2000 method is best matched to the way
18674 * the argument is handled internally and will deliver the
18675 * optimum resolution. The MJD method and the date & time methods
18676 * are both good compromises between resolution and convenience.
18677 *
18678 * <li> The CIO locator s is the difference between the right ascensions
18679 * of the same point in two systems: the two systems are the GCRS
18680 * and the CIP,CIO, and the point is the ascending node of the
18681 * CIP equator. The quantity s remains below 0.1 arcsecond
18682 * throughout 1900-2100.
18683 *
18684 * <li> The series used to compute s is in fact for s+XY/2, where X and Y
18685 * are the x and y components of the CIP unit vector; this series
18686 * is more compact than a direct series for s would be. This
18687 * function requires X,Y to be supplied by the caller, who is
18688 * responsible for providing values that are consistent with the
18689 * supplied date.
18690 *
18691 * <li> The model is consistent with the "P03" precession (Capitaine et
18692 * al. 2003), adopted by IAU 2006 Resolution 1, 2006, and the
18693 * IAU 2000A nutation (with P03 adjustments).
18694 *</ol>
18695 *<p>Called:<ul>
18696 * <li>{@link #jauFal03} mean anomaly of the Moon
18697 * <li>{@link #jauFalp03} mean anomaly of the Sun
18698 * <li>{@link #jauFaf03} mean argument of the latitude of the Moon
18699 * <li>{@link #jauFad03} mean elongation of the Moon from the Sun
18700 * <li>{@link #jauFaom03} mean longitude of the Moon's ascending node
18701 * <li>{@link #jauFave03} mean longitude of Venus
18702 * <li>{@link #jauFae03} mean longitude of Earth
18703 * <li>{@link #jauFapa03} general accumulated precession in longitude
18704 * </ul>
18705 *<p>References:
18706 *
18707 * <p>Capitaine, N., Wallace, P.T. & Chapront, J., 2003, Astron.
18708 * Astrophys. 432, 355
18709 *
18710 * <p>McCarthy, D.D., Petit, G. (eds.) 2004, IERS Conventions (2003),
18711 * IERS Technical Note No. 32, BKG
18712 *
18713 *@version 2009 December 17
18714 *
18715 * @since Release 20101201
18716 *
18717 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
18718 */
18719 public static double jauS06(double date1, double date2, double x, double y)
18720 {
18721 /* Time since J2000.0, in Julian centuries */
18722 double t;
18723
18724 /* Miscellaneous */
18725 int i, j;
18726 double a, w0, w1, w2, w3, w4, w5;
18727
18728 /* Fundamental arguments */
18729 double fa[] = new double[8];
18730
18731 /* Returned value */
18732 double s;
18733
18734 /* --------------------- */
18735 /* The series for s+XY/2 */
18736 /* --------------------- */
18737
18738 /* Polynomial coefficients */
18739 final double sp[] = {
18740
18741 /* 1-6 */
18742 94.00e-6,
18743 3808.65e-6,
18744 -122.68e-6,
18745 -72574.11e-6,
18746 27.98e-6,
18747 15.62e-6
18748 };
18749
18750 /* Terms of order t^0 */
18751 final TERM s0[] = {
18752
18753 /* 1-10 */
18754 new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, -2640.73e-6, 0.39e-6 ),
18755 new TERM(new int[]{ 0, 0, 0, 0, 2, 0, 0, 0}, -63.53e-6, 0.02e-6 ),
18756 new TERM(new int[]{ 0, 0, 2, -2, 3, 0, 0, 0}, -11.75e-6, -0.01e-6 ),
18757 new TERM(new int[]{ 0, 0, 2, -2, 1, 0, 0, 0}, -11.21e-6, -0.01e-6 ),
18758 new TERM(new int[]{ 0, 0, 2, -2, 2, 0, 0, 0}, 4.57e-6, 0.00e-6 ),
18759 new TERM(new int[]{ 0, 0, 2, 0, 3, 0, 0, 0}, -2.02e-6, 0.00e-6 ),
18760 new TERM(new int[]{ 0, 0, 2, 0, 1, 0, 0, 0}, -1.98e-6, 0.00e-6 ),
18761 new TERM(new int[]{ 0, 0, 0, 0, 3, 0, 0, 0}, 1.72e-6, 0.00e-6 ),
18762 new TERM(new int[]{ 0, 1, 0, 0, 1, 0, 0, 0}, 1.41e-6, 0.01e-6 ),
18763 new TERM(new int[]{ 0, 1, 0, 0, -1, 0, 0, 0}, 1.26e-6, 0.01e-6 ),
18764
18765 /* 11-20 */
18766 new TERM(new int[]{ 1, 0, 0, 0, -1, 0, 0, 0}, 0.63e-6, 0.00e-6 ),
18767 new TERM(new int[]{ 1, 0, 0, 0, 1, 0, 0, 0}, 0.63e-6, 0.00e-6 ),
18768 new TERM(new int[]{ 0, 1, 2, -2, 3, 0, 0, 0}, -0.46e-6, 0.00e-6 ),
18769 new TERM(new int[]{ 0, 1, 2, -2, 1, 0, 0, 0}, -0.45e-6, 0.00e-6 ),
18770 new TERM(new int[]{ 0, 0, 4, -4, 4, 0, 0, 0}, -0.36e-6, 0.00e-6 ),
18771 new TERM(new int[]{ 0, 0, 1, -1, 1, -8, 12, 0}, 0.24e-6, 0.12e-6 ),
18772 new TERM(new int[]{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.32e-6, 0.00e-6 ),
18773 new TERM(new int[]{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.28e-6, 0.00e-6 ),
18774 new TERM(new int[]{ 1, 0, 2, 0, 3, 0, 0, 0}, -0.27e-6, 0.00e-6 ),
18775 new TERM(new int[]{ 1, 0, 2, 0, 1, 0, 0, 0}, -0.26e-6, 0.00e-6 ),
18776
18777 /* 21-30 */
18778 new TERM(new int[]{ 0, 0, 2, -2, 0, 0, 0, 0}, 0.21e-6, 0.00e-6 ),
18779 new TERM(new int[]{ 0, 1, -2, 2, -3, 0, 0, 0}, -0.19e-6, 0.00e-6 ),
18780 new TERM(new int[]{ 0, 1, -2, 2, -1, 0, 0, 0}, -0.18e-6, 0.00e-6 ),
18781 new TERM(new int[]{ 0, 0, 0, 0, 0, 8,-13, -1}, 0.10e-6, -0.05e-6 ),
18782 new TERM(new int[]{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.15e-6, 0.00e-6 ),
18783 new TERM(new int[]{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.14e-6, 0.00e-6 ),
18784 new TERM(new int[]{ 0, 1, 2, -2, 2, 0, 0, 0}, 0.14e-6, 0.00e-6 ),
18785 new TERM(new int[]{ 1, 0, 0, -2, 1, 0, 0, 0}, -0.14e-6, 0.00e-6 ),
18786 new TERM(new int[]{ 1, 0, 0, -2, -1, 0, 0, 0}, -0.14e-6, 0.00e-6 ),
18787 new TERM(new int[]{ 0, 0, 4, -2, 4, 0, 0, 0}, -0.13e-6, 0.00e-6 ),
18788
18789 /* 31-33 */
18790 new TERM(new int[]{ 0, 0, 2, -2, 4, 0, 0, 0}, 0.11e-6, 0.00e-6 ),
18791 new TERM(new int[]{ 1, 0, -2, 0, -3, 0, 0, 0}, -0.11e-6, 0.00e-6 ),
18792 new TERM(new int[]{ 1, 0, -2, 0, -1, 0, 0, 0}, -0.11e-6, 0.00e-6 )
18793 };
18794
18795 /* Terms of order t^1 */
18796 final TERM s1[] = {
18797
18798 /* 1 - 3 */
18799 new TERM(new int[]{ 0, 0, 0, 0, 2, 0, 0, 0}, -0.07e-6, 3.57e-6 ),
18800 new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, 1.73e-6, -0.03e-6 ),
18801 new TERM(new int[]{ 0, 0, 2, -2, 3, 0, 0, 0}, 0.00e-6, 0.48e-6 )
18802 };
18803
18804 /* Terms of order t^2 */
18805 final TERM s2[] = {
18806
18807 /* 1-10 */
18808 new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, 743.52e-6, -0.17e-6 ),
18809 new TERM(new int[]{ 0, 0, 2, -2, 2, 0, 0, 0}, 56.91e-6, 0.06e-6 ),
18810 new TERM(new int[]{ 0, 0, 2, 0, 2, 0, 0, 0}, 9.84e-6, -0.01e-6 ),
18811 new TERM(new int[]{ 0, 0, 0, 0, 2, 0, 0, 0}, -8.85e-6, 0.01e-6 ),
18812 new TERM(new int[]{ 0, 1, 0, 0, 0, 0, 0, 0}, -6.38e-6, -0.05e-6 ),
18813 new TERM(new int[]{ 1, 0, 0, 0, 0, 0, 0, 0}, -3.07e-6, 0.00e-6 ),
18814 new TERM(new int[]{ 0, 1, 2, -2, 2, 0, 0, 0}, 2.23e-6, 0.00e-6 ),
18815 new TERM(new int[]{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.67e-6, 0.00e-6 ),
18816 new TERM(new int[]{ 1, 0, 2, 0, 2, 0, 0, 0}, 1.30e-6, 0.00e-6 ),
18817 new TERM(new int[]{ 0, 1, -2, 2, -2, 0, 0, 0}, 0.93e-6, 0.00e-6 ),
18818
18819 /* 11-20 */
18820 new TERM(new int[]{ 1, 0, 0, -2, 0, 0, 0, 0}, 0.68e-6, 0.00e-6 ),
18821 new TERM(new int[]{ 0, 0, 2, -2, 1, 0, 0, 0}, -0.55e-6, 0.00e-6 ),
18822 new TERM(new int[]{ 1, 0, -2, 0, -2, 0, 0, 0}, 0.53e-6, 0.00e-6 ),
18823 new TERM(new int[]{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.27e-6, 0.00e-6 ),
18824 new TERM(new int[]{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.27e-6, 0.00e-6 ),
18825 new TERM(new int[]{ 1, 0, -2, -2, -2, 0, 0, 0}, -0.26e-6, 0.00e-6 ),
18826 new TERM(new int[]{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.25e-6, 0.00e-6 ),
18827 new TERM(new int[]{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.22e-6, 0.00e-6 ),
18828 new TERM(new int[]{ 2, 0, 0, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 ),
18829 new TERM(new int[]{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.20e-6, 0.00e-6 ),
18830
18831 /* 21-25 */
18832 new TERM(new int[]{ 0, 0, 2, 2, 2, 0, 0, 0}, 0.17e-6, 0.00e-6 ),
18833 new TERM(new int[]{ 2, 0, 2, 0, 2, 0, 0, 0}, 0.13e-6, 0.00e-6 ),
18834 new TERM(new int[]{ 2, 0, 0, 0, 0, 0, 0, 0}, -0.13e-6, 0.00e-6 ),
18835 new TERM(new int[]{ 1, 0, 2, -2, 2, 0, 0, 0}, -0.12e-6, 0.00e-6 ),
18836 new TERM(new int[]{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.11e-6, 0.00e-6 )
18837 };
18838
18839 /* Terms of order t^3 */
18840 final TERM s3[] = {
18841
18842 /* 1-4 */
18843 new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, 0.30e-6, -23.42e-6 ),
18844 new TERM(new int[]{ 0, 0, 2, -2, 2, 0, 0, 0}, -0.03e-6, -1.46e-6 ),
18845 new TERM(new int[]{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.01e-6, -0.25e-6 ),
18846 new TERM(new int[]{ 0, 0, 0, 0, 2, 0, 0, 0}, 0.00e-6, 0.23e-6 )
18847 };
18848
18849 /* Terms of order t^4 */
18850 final TERM s4[] = {
18851
18852 /* 1-1 */
18853 new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.26e-6, -0.01e-6 )
18854 };
18855
18856 /* Number of terms in the series */
18857 final int NS0 = s0.length;
18858 final int NS1 = s1.length;
18859 final int NS2 = s2.length;
18860 final int NS3 = s3.length;
18861 final int NS4 = s4.length;
18862
18863 /*--------------------------------------------------------------------*/
18864
18865 /* Interval between fundamental epoch J2000.0 and current date (JC). */
18866 t = ((date1 - DJ00) + date2) / DJC;
18867
18868 /* Fundamental Arguments (from IERS Conventions 2003) */
18869
18870 /* Mean anomaly of the Moon. */
18871 fa[0] = jauFal03(t);
18872
18873 /* Mean anomaly of the Sun. */
18874 fa[1] = jauFalp03(t);
18875
18876 /* Mean longitude of the Moon minus that of the ascending node. */
18877 fa[2] = jauFaf03(t);
18878
18879 /* Mean elongation of the Moon from the Sun. */
18880 fa[3] = jauFad03(t);
18881
18882 /* Mean longitude of the ascending node of the Moon. */
18883 fa[4] = jauFaom03(t);
18884
18885 /* Mean longitude of Venus. */
18886 fa[5] = jauFave03(t);
18887
18888 /* Mean longitude of Earth. */
18889 fa[6] = jauFae03(t);
18890
18891 /* General precession in longitude. */
18892 fa[7] = jauFapa03(t);
18893
18894 /* Evaluate s. */
18895 w0 = sp[0];
18896 w1 = sp[1];
18897 w2 = sp[2];
18898 w3 = sp[3];
18899 w4 = sp[4];
18900 w5 = sp[5];
18901
18902 for (i = NS0-1; i >= 0; i--) {
18903 a = 0.0;
18904 for (j = 0; j < 8; j++) {
18905 a += (double)s0[i].nfa[j] * fa[j];
18906 }
18907 w0 += s0[i].s * sin(a) + s0[i].c * cos(a);
18908 }
18909
18910 for (i = NS1-1; i >= 0; i--) {
18911 a = 0.0;
18912 for (j = 0; j < 8; j++) {
18913 a += (double)s1[i].nfa[j] * fa[j];
18914 }
18915 w1 += s1[i].s * sin(a) + s1[i].c * cos(a);
18916 }
18917
18918 for (i = NS2-1; i >= 0; i--) {
18919 a = 0.0;
18920 for (j = 0; j < 8; j++) {
18921 a += (double)s2[i].nfa[j] * fa[j];
18922 }
18923 w2 += s2[i].s * sin(a) + s2[i].c * cos(a);
18924 }
18925
18926 for (i = NS3-1; i >= 0; i--) {
18927 a = 0.0;
18928 for (j = 0; j < 8; j++) {
18929 a += (double)s3[i].nfa[j] * fa[j];
18930 }
18931 w3 += s3[i].s * sin(a) + s3[i].c * cos(a);
18932 }
18933
18934 for (i = NS4-1; i >= 0; i--) {
18935 a = 0.0;
18936 for (j = 0; j < 8; j++) {
18937 a += (double)s4[i].nfa[j] * fa[j];
18938 }
18939 w4 += s4[i].s * sin(a) + s4[i].c * cos(a);
18940 }
18941
18942 s = (w0 +
18943 (w1 +
18944 (w2 +
18945 (w3 +
18946 (w4 +
18947 w5 * t) * t) * t) * t) * t) * DAS2R - x*y/2.0;
18948
18949 return s;
18950
18951 }
18952
18953
18954 /**
18955 * The CIO locator s, positioning the Celestial Intermediate Origin on
18956 * the equator of the Celestial Intermediate Pole, using the IAU 2006
18957 * precession and IAU 2000A nutation models.
18958 *
18959 *<p>This function is derived from the International Astronomical Union's
18960 * SOFA (Standards Of Fundamental Astronomy) software collection.
18961 *
18962 *<p>Status: support function.
18963 *
18964 *<!-- Given: -->
18965 * @param date1 double TT as a 2-part Julian Date (Note 1)
18966 * @param date2 double TT as a 2-part Julian Date (Note 1)
18967 *
18968 * <!-- Returned (function value): -->
18969 * @return double the CIO locator s in radians (Note 2)
18970 *
18971 * <p>Notes:
18972 * <ol>
18973 *
18974 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
18975 * convenient way between the two arguments. For example,
18976 * JD(TT)=2450123.7 could be expressed in any of these ways,
18977 * among others:
18978 *<pre>
18979 * date1 date2
18980 *
18981 * 2450123.7 0.0 (JD method)
18982 * 2451545.0 -1421.3 (J2000 method)
18983 * 2400000.5 50123.2 (MJD method)
18984 * 2450123.5 0.2 (date & time method)
18985 *</pre>
18986 * The JD method is the most natural and convenient to use in
18987 * cases where the loss of several decimal digits of resolution
18988 * is acceptable. The J2000 method is best matched to the way
18989 * the argument is handled internally and will deliver the
18990 * optimum resolution. The MJD method and the date & time methods
18991 * are both good compromises between resolution and convenience.
18992 *
18993 * <li> The CIO locator s is the difference between the right ascensions
18994 * of the same point in two systems. The two systems are the GCRS
18995 * and the CIP,CIO, and the point is the ascending node of the
18996 * CIP equator. The CIO locator s remains a small fraction of
18997 * 1 arcsecond throughout 1900-2100.
18998 *
18999 * <li> The series used to compute s is in fact for s+XY/2, where X and Y
19000 * are the x and y components of the CIP unit vector; this series is
19001 * more compact than a direct series for s would be. The present
19002 * function uses the full IAU 2000A nutation model when predicting
19003 * the CIP position.
19004 *</ol>
19005 *<p>Called:<ul>
19006 * <li>{@link #jauPnm06a} classical NPB matrix, IAU 2006/2000A
19007 * <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
19008 * <li>{@link #jauS06} the CIO locator s, given X,Y, IAU 2006
19009 * </ul>
19010 *<p>References:
19011 *
19012 * <p>Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
19013 * "Expressions for the Celestial Intermediate Pole and Celestial
19014 * Ephemeris Origin consistent with the IAU 2000A precession-
19015 * nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
19016 *
19017 * n.b. The celestial ephemeris origin (CEO) was renamed "celestial
19018 * intermediate origin" (CIO) by IAU 2006 Resolution 2.
19019 *
19020 * <p>Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
19021 *
19022 * <p>McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
19023 * IERS Technical Note No. 32, BKG
19024 *
19025 * <p>Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
19026 *
19027 *@version 2010 January 18
19028 *
19029 * @since Release 20101201
19030 *
19031 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19032 */
19033 public static double jauS06a(double date1, double date2)
19034 {
19035 double rnpb[][] = new double[3][3], s;
19036
19037
19038 /* Bias-precession-nutation-matrix, IAU 20006/2000A. */
19039 rnpb = jauPnm06a(date1, date2);
19040
19041 /* Extract the CIP coordinates. */
19042 CelestialIntermediatePole cip = jauBpn2xy(rnpb);
19043
19044 /* Compute the CIO locator s, given the CIP coordinates. */
19045 s = jauS06(date1, date2, cip.x, cip.y);
19046
19047 return s;
19048
19049 }
19050
19051
19052 /**
19053 * Convert spherical coordinates to Cartesian.
19054 *
19055 *<p>This function is derived from the International Astronomical Union's
19056 * SOFA (Standards Of Fundamental Astronomy) software collection.
19057 *
19058 *<p>Status: vector/matrix support function.
19059 *
19060 *<!-- Given: -->
19061 * @param theta double longitude angle (radians)
19062 * @param phi double latitude angle (radians)
19063 *
19064 *<!-- Returned: -->
19065 * @return c double[3] <u>returned</u> direction cosines
19066 *
19067 *@version 2008 October 28
19068 *
19069 * @since Release 20101201
19070 *
19071 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19072 */
19073 public static double[] jauS2c(double theta, double phi )
19074 {
19075 double cp, c[] = new double[3];
19076
19077
19078 cp = cos(phi);
19079 c[0] = cos(theta) * cp;
19080 c[1] = sin(theta) * cp;
19081 c[2] = sin(phi);
19082
19083 return c;
19084
19085 }
19086
19087
19088 /**
19089 * Convert spherical polar coordinates to p-vector.
19090 *
19091 *<p>This function is derived from the International Astronomical Union's
19092 * SOFA (Standards Of Fundamental Astronomy) software collection.
19093 *
19094 *<p>Status: vector/matrix support function.
19095 *
19096 *<!-- Given: -->
19097 * @param theta double longitude angle (radians)
19098 * @param phi double latitude angle (radians)
19099 * @param r double radial distance
19100 *
19101 *<!-- Returned: -->
19102 * @return p double[3] <u>returned</u> Cartesian coordinates
19103 *
19104 *<p>Called:<ul>
19105 * <li>{@link #jauS2c} spherical coordinates to unit vector
19106 * <li>{@link #jauSxp} multiply p-vector by scalar
19107 * </ul>
19108 *@version 2008 May 11
19109 *
19110 * @since Release 20101201
19111 *
19112 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19113 */
19114 public static double[] jauS2p(double theta, double phi, double r )
19115 {
19116 double p[];
19117 double u[] = new double[3];
19118
19119
19120 u = jauS2c(theta,phi);
19121 p = jauSxp(r,u);
19122
19123 return p;
19124
19125 }
19126
19127
19128 /**
19129 * Convert position/velocity from spherical to Cartesian coordinates.
19130 *
19131 *<p>This function is derived from the International Astronomical Union's
19132 * SOFA (Standards Of Fundamental Astronomy) software collection.
19133 *
19134 *<p>Status: vector/matrix support function.
19135 *
19136 *<!-- Given: -->
19137 * @param theta double longitude angle (radians)
19138 * @param phi double latitude angle (radians)
19139 * @param r double radial distance
19140 * @param td double rate of change of theta
19141 * @param pd double rate of change of phi
19142 * @param rd double rate of change of r
19143 *
19144 *<!-- Returned: -->
19145 * @return pv double[2][3] <u>returned</u> pv-vector
19146 *
19147 *@version 2008 May 25
19148 *
19149 * @since Release 20101201
19150 *
19151 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19152 */
19153 public static double[][] jauS2pv(double theta, double phi, double r,
19154 double td, double pd, double rd)
19155 {
19156 double pv[][] = new double[2][3];
19157 double st, ct, sp, cp, rcp, x, y, rpd, w;
19158
19159
19160 st = sin(theta);
19161 ct = cos(theta);
19162 sp = sin(phi);
19163 cp = cos(phi);
19164 rcp = r * cp;
19165 x = rcp * ct;
19166 y = rcp * st;
19167 rpd = r * pd;
19168 w = rpd*sp - cp*rd;
19169
19170 pv[0][0] = x;
19171 pv[0][1] = y;
19172 pv[0][2] = r * sp;
19173 pv[1][0] = -y*td - w*ct;
19174 pv[1][1] = x*td - w*st;
19175 pv[1][2] = rpd*cp + sp*rd;
19176
19177 return pv;
19178
19179 }
19180
19181
19182 /**
19183 * Multiply a pv-vector by two scalars.
19184 *
19185 *<p>This function is derived from the International Astronomical Union's
19186 * SOFA (Standards Of Fundamental Astronomy) software collection.
19187 *
19188 *<p>Status: vector/matrix support function.
19189 *
19190 *<!-- Given: -->
19191 * @param s1 double scalar to multiply position component by
19192 * @param s2 double scalar to multiply velocity component by
19193 * @param pv double[2][3] pv-vector
19194 *
19195 *<!-- Returned: -->
19196 * @return spv double[2][3] <u>returned</u> pv-vector: p scaled by s1, v scaled by s2
19197 *
19198 * Note:
19199 * It is permissible for pv and spv to be the same array.
19200 *
19201 *<p>Called:<ul>
19202 * <li>{@link #jauSxp} multiply p-vector by scalar
19203 * </ul>
19204 *@version 2008 October 28
19205 *
19206 * @since Release 20101201
19207 *
19208 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19209 */
19210 public static double[][] jauS2xpv(double s1, double s2, double pv[][])
19211 {
19212 double spv[][] = new double[2][3];
19213 spv[0] = jauSxp(s1, pv[0]);
19214 spv[1] =jauSxp(s2, pv[1]);
19215
19216 return spv;
19217
19218 }
19219
19220
19221 /**
19222 * Angular separation between two p-vectors.
19223 *
19224 *<p>This function is derived from the International Astronomical Union's
19225 * SOFA (Standards Of Fundamental Astronomy) software collection.
19226 *
19227 *<p>Status: vector/matrix support function.
19228 *
19229 *<!-- Given: -->
19230 * @param a double[3] first p-vector (not necessarily unit length)
19231 * @param b double[3] second p-vector (not necessarily unit length)
19232 *
19233 * <!-- Returned (function value): -->
19234 * @return double angular separation (radians, always positive)
19235 *
19236 * <p>Notes:
19237 * <ol>
19238 *
19239 * <li> If either vector is null, a zero result is returned.
19240 *
19241 * <li> The angular separation is most simply formulated in terms of
19242 * scalar product. However, this gives poor accuracy for angles
19243 * near zero and pi. The present algorithm uses both cross product
19244 * and dot product, to deliver full accuracy whatever the size of
19245 * the angle.
19246 *</ol>
19247 *<p>Called:<ul>
19248 * <li>{@link #jauPxp} vector product of two p-vectors
19249 * <li>{@link #jauPm} modulus of p-vector
19250 * <li>{@link #jauPdp} scalar product of two p-vectors
19251 * </ul>
19252 *@version 2008 May 22
19253 *
19254 * @since Release 20101201
19255 *
19256 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19257 */
19258 public static double jauSepp(double a[] , double b[] )
19259 {
19260 double axb[] = new double[3], ss, cs, s;
19261
19262
19263 /* Sine of angle between the vectors, multiplied by the two moduli. */
19264 axb = jauPxp(a,b);
19265 ss = jauPm(axb);
19266
19267 /* Cosine of the angle, multiplied by the two moduli. */
19268 cs = jauPdp(a, b);
19269
19270 /* The angle. */
19271 s = ((ss != 0.0) || (cs != 0.0)) ? atan2(ss, cs) : 0.0;
19272
19273 return s;
19274
19275 }
19276
19277
19278 /**
19279 * Angular separation between two sets of spherical coordinates.
19280 *
19281 *<p>This function is derived from the International Astronomical Union's
19282 * SOFA (Standards Of Fundamental Astronomy) software collection.
19283 *
19284 *<p>Status: vector/matrix support function.
19285 *
19286 *<!-- Given: -->
19287 * @param al double first longitude (radians)
19288 * @param ap double first latitude (radians)
19289 * @param bl double second longitude (radians)
19290 * @param bp double second latitude (radians)
19291 *
19292 * <!-- Returned (function value): -->
19293 * @return double angular separation (radians)
19294 *
19295 *<p>Called:<ul>
19296 * <li>{@link #jauS2c} spherical coordinates to unit vector
19297 * <li>{@link #jauSepp} angular separation between two p-vectors
19298 * </ul>
19299 *@version 2008 May 16
19300 *
19301 * @since Release 20101201
19302 *
19303 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19304 */
19305 public static double jauSeps(double al, double ap, double bl, double bp)
19306 {
19307 double ac[] = new double[3], bc[] = new double[3], s;
19308
19309
19310 /* Spherical to Cartesian. */
19311 ac = jauS2c(al,ap);
19312 bc = jauS2c(bl,bp);
19313
19314 /* Angle between the vectors. */
19315 s = jauSepp(ac, bc);
19316
19317 return s;
19318
19319 }
19320
19321
19322 /**
19323 * The TIO locator s', positioning the Terrestrial Intermediate Origin
19324 * on the equator of the Celestial Intermediate Pole.
19325 *
19326 *<p>This function is derived from the International Astronomical Union's
19327 * SOFA (Standards Of Fundamental Astronomy) software collection.
19328 *
19329 *<p>Status: canonical model.
19330 *
19331 *<!-- Given: -->
19332 * @param date1 double TT as a 2-part Julian Date (Note 1)
19333 * @param date2 double TT as a 2-part Julian Date (Note 1)
19334 *
19335 * <!-- Returned (function value): -->
19336 * @return double the TIO locator s' in radians (Note 2)
19337 *
19338 * <p>Notes:
19339 * <ol>
19340 *
19341 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
19342 * convenient way between the two arguments. For example,
19343 * JD(TT)=2450123.7 could be expressed in any of these ways,
19344 * among others:
19345 *<pre>
19346 * date1 date2
19347 *
19348 * 2450123.7 0.0 (JD method)
19349 * 2451545.0 -1421.3 (J2000 method)
19350 * 2400000.5 50123.2 (MJD method)
19351 * 2450123.5 0.2 (date & time method)
19352 *</pre>
19353 * The JD method is the most natural and convenient to use in
19354 * cases where the loss of several decimal digits of resolution
19355 * is acceptable. The J2000 method is best matched to the way
19356 * the argument is handled internally and will deliver the
19357 * optimum resolution. The MJD method and the date & time methods
19358 * are both good compromises between resolution and convenience.
19359 *
19360 * <li> The TIO locator s' is obtained from polar motion observations by
19361 * numerical integration, and so is in essence unpredictable.
19362 * However, it is dominated by a secular drift of about
19363 * 47 microarcseconds per century, which is the approximation
19364 * evaluated by the present function.
19365 *</ol>
19366 *<p>Reference:
19367 *
19368 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
19369 * IERS Technical Note No. 32, BKG (2004)
19370 *
19371 *@version 2008 May 24
19372 *
19373 * @since Release 20101201
19374 *
19375 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19376 */
19377 public static double jauSp00(double date1, double date2)
19378 {
19379 double t, sp;
19380
19381
19382 /* Interval between fundamental epoch J2000.0 and current date (JC). */
19383 t = ((date1 - DJ00) + date2) / DJC;
19384
19385 /* Approximate s'. */
19386 sp = -47e-6 * t * DAS2R;
19387
19388 return sp;
19389
19390 }
19391
19392
19393 /**
19394 * Star proper motion: update star catalog data for space motion.
19395 *
19396 *<p>This function is derived from the International Astronomical Union's
19397 * SOFA (Standards Of Fundamental Astronomy) software collection.
19398 *
19399 *<p>Status: support function.
19400 *
19401 *<!-- Given: -->
19402 * @param ra1 double right ascension (radians), before
19403 * @param dec1 double declination (radians), before
19404 * @param pmr1 double RA proper motion (radians/year), before
19405 * @param pmd1 double Dec proper motion (radians/year), before
19406 * @param px1 double parallax (arcseconds), before
19407 * @param rv1 double radial velocity (km/s, +ve = receding), before
19408 * @param ep1a double "before" epoch, part A (Note 1)
19409 * @param ep1b double "before" epoch, part B (Note 1)
19410 * @param ep2a double "after" epoch, part A (Note 1)
19411 * @param ep2b double "after" epoch, part B (Note 1)
19412 *
19413 *<!-- Returned: -->
19414 * @return ra2 double <u>returned</u> right ascension (radians), after
19415 * dec2 double <u>returned</u> declination (radians), after
19416 * pmr2 double <u>returned</u> RA proper motion (radians/year), after
19417 * pmd2 double <u>returned</u> Dec proper motion (radians/year), after
19418 * px2 double <u>returned</u> parallax (arcseconds), after
19419 * rv2 double <u>returned</u> radial velocity (km/s, +ve = receding), after
19420 *
19421 * <!-- Returned (function value): -->
19422 * @return int status:
19423 * -1 = system error (should not occur)
19424 * 0 = no warnings or errors
19425 * 1 = distance overridden (Note 6)
19426 * 2 = excessive velocity (Note 7)
19427 * 4 = solution didn't converge (Note 8)
19428 * else = binary logical OR of the above warnings
19429 *FIXME need to return the status as well.
19430 * <p>Notes:
19431 * <ol>
19432 *
19433 * <li> The starting and ending TDB dates ep1a+ep1b and ep2a+ep2b are
19434 * Julian Dates, apportioned in any convenient way between the two
19435 * parts (A and B). For example, JD(TDB)=2450123.7 could be
19436 * expressed in any of these ways, among others:
19437 *<pre>
19438 * epna epnb
19439 *
19440 * 2450123.7 0.0 (JD method)
19441 * 2451545.0 -1421.3 (J2000 method)
19442 * 2400000.5 50123.2 (MJD method)
19443 * 2450123.5 0.2 (date & time method)
19444 *</pre>
19445 * The JD method is the most natural and convenient to use in
19446 * cases where the loss of several decimal digits of resolution
19447 * is acceptable. The J2000 method is best matched to the way
19448 * the argument is handled internally and will deliver the
19449 * optimum resolution. The MJD method and the date & time methods
19450 * are both good compromises between resolution and convenience.
19451 *
19452 * <li> In accordance with normal star-catalog conventions, the object's
19453 * right ascension and declination are freed from the effects of
19454 * secular aberration. The frame, which is aligned to the catalog
19455 * equator and equinox, is Lorentzian and centered on the SSB.
19456 *
19457 * The proper motions are the rate of change of the right ascension
19458 * and declination at the catalog epoch and are in radians per TDB
19459 * Julian year.
19460 *
19461 * The parallax and radial velocity are in the same frame.
19462 *
19463 * <li> Care is needed with units. The star coordinates are in radians
19464 * and the proper motions in radians per Julian year, but the
19465 * parallax is in arcseconds.
19466 *
19467 * <li> The RA proper motion is in terms of coordinate angle, not true
19468 * angle. If the catalog uses arcseconds for both RA and Dec proper
19469 * motions, the RA proper motion will need to be divided by cos(Dec)
19470 * before use.
19471 *
19472 * <li> Straight-line motion at constant speed, in the inertial frame,
19473 * is assumed.
19474 *
19475 * <li> An extremely small (or zero or negative) parallax is interpreted
19476 * to mean that the object is on the "celestial sphere", the radius
19477 * of which is an arbitrary (large) value (see the jauStarpv
19478 * function for the value used). When the distance is overridden in
19479 * this way, the status, initially zero, has 1 added to it.
19480 *
19481 * <li> If the space velocity is a significant fraction of c (see the
19482 * constant VMAX in the function jauStarpv), it is arbitrarily set
19483 * to zero. When this action occurs, 2 is added to the status.
19484 *
19485 * <li> The relativistic adjustment carried out in the jauStarpv function
19486 * involves an iterative calculation. If the process fails to
19487 * converge within a set number of iterations, 4 is added to the
19488 * status.
19489 *</ol>
19490 *<p>Called:<ul>
19491 * <li>{@link #jauStarpv} star catalog data to space motion pv-vector
19492 * <li>{@link #jauPvu} update a pv-vector
19493 * <li>{@link #jauPdp} scalar product of two p-vectors
19494 * <li>{@link #jauPvstar} space motion pv-vector to star catalog data
19495 * </ul>
19496 *@version 2008 May 16
19497 *
19498 * @since Release 20101201
19499 *
19500 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19501 */
19502 public static CatalogCoords jauStarpm(double ra1, double dec1,
19503 double pmr1, double pmd1, double px1, double rv1,
19504 double ep1a, double ep1b, double ep2a, double ep2b) throws JSOFAInternalError
19505 {
19506 double pv1[][] = new double[2][3], tl1, dt, pv[][] = new double[2][3], r2, rdv, v2, c2mv2, tl2,
19507 pv2[][] = new double[2][3];
19508 jauStarpv(ra1, dec1, pmr1, pmd1, px1, rv1, pv1);
19509
19510 /* Light time when observed (days). */
19511 tl1 = jauPm(pv1[0]) / DC;
19512
19513 /* Time interval, "before" to "after" (days). */
19514 dt = (ep2a - ep1a) + (ep2b - ep1b);
19515
19516 /* Move star along track from the "before" observed position to the */
19517 /* "after" geometric position. */
19518 pv = jauPvu(dt + tl1, pv1);
19519
19520 /* From this geometric position, deduce the observed light time (days) */
19521 /* at the "after" epoch (with theoretically unneccessary error check). */
19522 r2 = jauPdp(pv[0], pv[0]);
19523 rdv = jauPdp(pv[0], pv[1]);
19524 v2 = jauPdp(pv[1], pv[1]);
19525 c2mv2 = DC*DC - v2;
19526 if (c2mv2 <= 0) throw new JSOFAInternalError("internal error", -1);
19527 tl2 = (-rdv + sqrt(rdv*rdv + c2mv2*r2)) / c2mv2;
19528
19529 /* Move the position along track from the observed place at the */
19530 /* "before" epoch to the observed place at the "after" epoch. */
19531 pv2 =jauPvu(dt + (tl1 - tl2), pv1 );
19532
19533 /* Space motion pv-vector to RA,Dec etc. at the "after" epoch. */
19534 CatalogCoords cat = jauPvstar(pv2);
19535
19536 return cat;
19537
19538 }
19539
19540
19541 /**
19542 * Convert star catalog coordinates to position+velocity vector.
19543 *
19544 *<p>This function is derived from the International Astronomical Union's
19545 * SOFA (Standards Of Fundamental Astronomy) software collection.
19546 *
19547 *<p>Status: support function.
19548 *
19549 * Given (Note 1):
19550 * ra double right ascension (radians)
19551 * dec double declination (radians)
19552 * pmr double RA proper motion (radians/year)
19553 * pmd double Dec proper motion (radians/year)
19554 * px double parallax (arcseconds)
19555 * rv double radial velocity (km/s, positive = receding)
19556 *
19557 * Returned (Note 2):
19558 * pv double[2][3] pv-vector (AU, AU/day)
19559 *
19560 * <!-- Returned (function value): -->
19561 * @return int status:
19562 * 0 = no warnings
19563 * 1 = distance overridden (Note 6)
19564 * 2 = excessive speed (Note 7)
19565 * 4 = solution didn't converge (Note 8)
19566 * else = binary logical OR of the above
19567 *
19568 * <p>Notes:
19569 * <ol>
19570 *
19571 * <li> The star data accepted by this function are "observables" for an
19572 * imaginary observer at the solar-system barycenter. Proper motion
19573 * and radial velocity are, strictly, in terms of barycentric
19574 * coordinate time, TCB. For most practical applications, it is
19575 * permissible to neglect the distinction between TCB and ordinary
19576 * "proper" time on Earth (TT/TAI). The result will, as a rule, be
19577 * limited by the intrinsic accuracy of the proper-motion and
19578 * radial-velocity data; moreover, the pv-vector is likely to be
19579 * merely an intermediate result, so that a change of time unit
19580 * would cancel out overall.
19581 *
19582 * In accordance with normal star-catalog conventions, the object's
19583 * right ascension and declination are freed from the effects of
19584 * secular aberration. The frame, which is aligned to the catalog
19585 * equator and equinox, is Lorentzian and centered on the SSB.
19586 *
19587 * <li> The resulting position and velocity pv-vector is with respect to
19588 * the same frame and, like the catalog coordinates, is freed from
19589 * the effects of secular aberration. Should the "coordinate
19590 * direction", where the object was located at the catalog epoch, be
19591 * required, it may be obtained by calculating the magnitude of the
19592 * position vector pv[0][0-2] dividing by the speed of light in
19593 * AU/day to give the light-time, and then multiplying the space
19594 * velocity pv[1][0-2] by this light-time and adding the result to
19595 * pv[0][0-2].
19596 *
19597 * Summarizing, the pv-vector returned is for most stars almost
19598 * identical to the result of applying the standard geometrical
19599 * "space motion" transformation. The differences, which are the
19600 * subject of the Stumpff paper referenced below, are:
19601 *
19602 * (i) In stars with significant radial velocity and proper motion,
19603 * the constantly changing light-time distorts the apparent proper
19604 * motion. Note that this is a classical, not a relativistic,
19605 * effect.
19606 *
19607 * (ii) The transformation complies with special relativity.
19608 *
19609 * <li> Care is needed with units. The star coordinates are in radians
19610 * and the proper motions in radians per Julian year, but the
19611 * parallax is in arcseconds; the radial velocity is in km/s, but
19612 * the pv-vector result is in AU and AU/day.
19613 *
19614 * <li> The RA proper motion is in terms of coordinate angle, not true
19615 * angle. If the catalog uses arcseconds for both RA and Dec proper
19616 * motions, the RA proper motion will need to be divided by cos(Dec)
19617 * before use.
19618 *
19619 * <li> Straight-line motion at constant speed, in the inertial frame,
19620 * is assumed.
19621 *
19622 * <li> An extremely small (or zero or negative) parallax is interpreted
19623 * to mean that the object is on the "celestial sphere", the radius
19624 * of which is an arbitrary (large) value (see the constant PXMIN).
19625 * When the distance is overridden in this way, the status,
19626 * initially zero, has 1 added to it.
19627 *
19628 * <li> If the space velocity is a significant fraction of c (see the
19629 * constant VMAX), it is arbitrarily set to zero. When this action
19630 * occurs, 2 is added to the status.
19631 *
19632 * <li> The relativistic adjustment involves an iterative calculation.
19633 * If the process fails to converge within a set number (IMAX) of
19634 * iterations, 4 is added to the status.
19635 *
19636 * <li> The inverse transformation is performed by the function
19637 * jauPvstar.
19638 *</ol>
19639 *<p>Called:<ul>
19640 * <li>{@link #jauS2pv} spherical coordinates to pv-vector
19641 * <li>{@link #jauPm} modulus of p-vector
19642 * <li>{@link #jauZp} zero p-vector
19643 * <li>{@link #jauPn} decompose p-vector into modulus and direction
19644 * <li>{@link #jauPdp} scalar product of two p-vectors
19645 * <li>{@link #jauSxp} multiply p-vector by scalar
19646 * <li>{@link #jauPmp} p-vector minus p-vector
19647 * <li>{@link #jauPpp} p-vector plus p-vector
19648 * </ul>
19649 *<p>Reference:
19650 *
19651 * Stumpff, P., 1985, Astron.Astrophys. 144, 232-240.
19652 *
19653 *@version 2009 July 6
19654 *
19655 * @since Release 20101201
19656 *
19657 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19658 */
19659 public static int jauStarpv(double ra, double dec,
19660 double pmr, double pmd, double px, double rv,
19661 double pv[][])
19662 {
19663 /* Smallest allowed parallax */
19664 final double PXMIN = 1e-7;
19665
19666 /* Largest allowed speed (fraction of c) */
19667 final double VMAX = 0.5;
19668
19669 /* Maximum number of iterations for relativistic solution */
19670 final int IMAX = 100;
19671
19672 int i, iwarn;
19673 double w, r, rd, rad, decd, v, x[] = new double[3], usr[] = new double[3], ust[] = new double[3],
19674 vsr, vst, betst, betsr, bett, betr,
19675 dd, ddel, ur[] = new double[3], ut[] = new double[3],
19676 d = 0.0, del = 0.0, /* to prevent */
19677 odd = 0.0, oddel = 0.0, /* compiler */
19678 od = 0.0, odel = 0.0; /* warnings */
19679
19680
19681 /* Distance (AU). */
19682 if (px >= PXMIN) {
19683 w = px;
19684 iwarn = 0;
19685 } else {
19686 w = PXMIN;
19687 iwarn = 1;
19688 }
19689 r = DR2AS / w;
19690
19691 /* Radial velocity (AU/day). */
19692 rd = DAYSEC * rv * 1e3 / DAU;
19693
19694 /* Proper motion (radian/day). */
19695 rad = pmr / DJY;
19696 decd = pmd / DJY;
19697
19698 /* To pv-vector (AU,AU/day). */
19699 double[][] pvt = jauS2pv(ra, dec, r, rad, decd, rd);
19700 jauCpv(pvt,pv);
19701
19702 /* If excessive velocity, arbitrarily set it to zero. */
19703 v = jauPm(pv[1]);
19704 if (v / DC > VMAX) {
19705 jauZp(pv[1]);
19706 iwarn += 2;
19707 }
19708
19709 /* Isolate the radial component of the velocity (AU/day). */
19710 NormalizedVector nv = jauPn(pv[0]);
19711 w = nv.r;
19712 x = nv.u;
19713 vsr = jauPdp(x, pv[1]);
19714 usr = jauSxp(vsr,x);
19715
19716 /* Isolate the transverse component of the velocity (AU/day). */
19717 ust = jauPmp(pv[1], usr);
19718 vst = jauPm(ust);
19719
19720 /* Special-relativity dimensionless parameters. */
19721 betsr = vsr / DC;
19722 betst = vst / DC;
19723
19724 /* Determine the inertial-to-observed relativistic correction terms. */
19725 bett = betst;
19726 betr = betsr;
19727 for (i = 0; i < IMAX; i++) {
19728 d = 1.0 + betr;
19729 del = sqrt(1.0 - betr*betr - bett*bett) - 1.0;
19730 betr = d * betsr + del;
19731 bett = d * betst;
19732 if (i > 0) {
19733 dd = abs(d - od);
19734 ddel = abs(del - odel);
19735 if ((i > 1) && (dd >= odd) && (ddel >= oddel)) break;
19736 odd = dd;
19737 oddel = ddel;
19738 }
19739 od = d;
19740 odel = del;
19741 }
19742 if (i >= IMAX) iwarn += 4;
19743
19744 /* Replace observed radial velocity with inertial value. */
19745 w = (betsr != 0.0) ? d + del / betsr : 1.0;
19746 ur = jauSxp(w,usr);
19747
19748 /* Replace observed tangential velocity with inertial value. */
19749 ut = jauSxp(d,ust);
19750
19751 /* Combine the two to obtain the inertial space velocity. */
19752 pv[1] = jauPpp(ur, ut);
19753
19754 /* Return the status. */
19755 return iwarn;
19756
19757 }
19758
19759
19760 /**
19761 * Multiply a p-vector by a scalar.
19762 *
19763 *<p>This function is derived from the International Astronomical Union's
19764 * SOFA (Standards Of Fundamental Astronomy) software collection.
19765 *
19766 *<p>Status: vector/matrix support function.
19767 *
19768 *<!-- Given: -->
19769 * @param s double scalar
19770 * @param p double[3] p-vector
19771 *
19772 *<!-- Returned: -->
19773 * @return sp double[3] <u>returned</u> s * p
19774 *
19775 *
19776 *
19777 *@version 2008 October 28
19778 *
19779 * @since Release 20101201
19780 *
19781 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19782 */
19783 public static double[] jauSxp(double s, double p[])
19784 {
19785 double sp[] = new double[3];
19786 sp[0] = s * p[0];
19787 sp[1] = s * p[1];
19788 sp[2] = s * p[2];
19789
19790 return sp;
19791
19792 }
19793
19794
19795 /**
19796 * Multiply a pv-vector by a scalar.
19797 *
19798 *<p>This function is derived from the International Astronomical Union's
19799 * SOFA (Standards Of Fundamental Astronomy) software collection.
19800 *
19801 *<p>Status: vector/matrix support function.
19802 *
19803 *<!-- Given: -->
19804 * @param s double scalar
19805 * @param pv double[2][3] pv-vector
19806 *
19807 *<!-- Returned: -->
19808 * @return spv double[2][3] <u>returned</u> s * pv
19809 *
19810 * Note:
19811 * It is permissible for pv and psv to be the same array
19812 *
19813 *<p>Called:<ul>
19814 * <li>{@link #jauS2xpv} multiply pv-vector by two scalars
19815 * </ul>
19816 *@version 2008 October 28
19817 *
19818 * @since Release 20101201
19819 *
19820 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19821 */
19822 public static double[][] jauSxpv(double s, double pv[][])
19823 {
19824 double spv[][];
19825 spv = jauS2xpv(s, s, pv);
19826
19827 return spv;
19828
19829 }
19830
19831 /**
19832 *
19833 * Time scale transformation: International Atomic Time, TAI, to
19834 * Terrestrial Time, TT.
19835 *
19836 * <p>This function is derived from the International Astronomical Union's
19837 * SOFA (Standards of Fundamental Astronomy) software collection.
19838 *
19839 *<p>Status: canonical.
19840 *
19841 *<!-- Given: -->
19842 * @param tai1 double TAI as a 2-part Julian Date
19843 * @param tai2 double TAI as a 2-part Julian Date
19844 *
19845 *<!-- Returned:-->
19846 * @return JulianDate TT as a 2-part Julian Date
19847 *
19848 *
19849 * Note:
19850 *
19851 * tai1+tai2 is Julian Date, apportioned in any convenient way
19852 * between the two arguments, for example where tai1 is the Julian
19853 * Day Number and tai2 is the fraction of a day. The returned
19854 * tt1,tt2 follow suit.
19855 *
19856 *<p>References:
19857 *
19858 * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
19859 * IERS Technical Note No. 32, BKG (2004)
19860 *
19861 * Explanatory Supplement to the Astronomical Almanac,
19862 * P. Kenneth Seidelmann (ed), University Science Books (1992)
19863 *
19864 *@version 2010 May 16
19865 *
19866 *@since SOFA release 2010-12-01
19867 *
19868 * <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
19869 */
19870 public static JulianDate jauTaitt(double tai1, double tai2)
19871 {
19872
19873 double tt1, tt2;
19874 /* TT minus TAI (days). */
19875 final double dtat = TTMTAI / DAYSEC;
19876
19877 /* Result, safeguarding precision. */
19878
19879 if ( tai1 > tai2 ) {
19880 tt1 = tai1;
19881 tt2 = tai2 + dtat;
19882 } else {
19883 tt1 = tai1 + dtat;
19884 tt2 = tai2;
19885 }
19886
19887
19888 return new JulianDate(tt1, tt2);
19889 };
19890
19891 /**
19892 *
19893 * Time scale transformation: International Atomic Time, TAI, to
19894 * Universal Time, UT1.
19895 *
19896 * <p>This function is derived from the International Astronomical Union's
19897 * SOFA (Standards of Fundamental Astronomy) software collection.
19898 *
19899 *<p>Status: canonical.
19900 *
19901 *<!-- Given: -->
19902 * @param tai1 double TAI as a 2-part Julian Date
19903 * @param tai2 double TAI as a 2-part Julian Date
19904 * @param dta double UT1-TAI in seconds
19905 *
19906 *<!-- Returned:-->
19907 * @return UT1 as a 2-part Julian Date
19908 *
19909 *
19910 *<p>Notes:
19911 * <ol>
19912 * <li> tai1+tai2 is Julian Date, apportioned in any convenient way
19913 * between the two arguments, for example where tai1 is the Julian
19914 * Day Number and tai2 is the fraction of a day. The returned
19915 * UT11,UT12 follow suit.
19916 *
19917 * <li> The argument dta, i.e. UT1-TAI, is an observed quantity, and is
19918 * available from IERS tabulations.
19919 * </ol>
19920 * Reference:
19921 *
19922 * Explanatory Supplement to the Astronomical Almanac,
19923 * P. Kenneth Seidelmann (ed), University Science Books (1992)
19924 *
19925 *@version 2010 May 16
19926 *
19927 *@since SOFA release 2010-12-01
19928 *
19929 * <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
19930 *
19931 */
19932 public static JulianDate jauTaiut1(double tai1, double tai2, double dta)
19933
19934 {
19935 double dtad,ut11, ut12;
19936
19937
19938 /* Result, safeguarding precision. */
19939 dtad = dta / DAYSEC;
19940 if ( tai1 > tai2 ) {
19941 ut11 = tai1;
19942 ut12 = tai2 + dtad;
19943 } else {
19944 ut11 = tai1 + dtad;
19945 ut12 = tai2;
19946 }
19947
19948 return new JulianDate(ut11, ut12);
19949 };
19950
19951 /**
19952 *
19953 * Time scale transformation: International Atomic Time, TAI, to
19954 * Coordinated Universal Time, UTC.
19955 *
19956 * <p>This function is derived from the International Astronomical Union's
19957 * SOFA (Standards of Fundamental Astronomy) software collection.
19958 *
19959 *<p>Status: canonical.
19960 *
19961 *<!-- Given: -->
19962 * @param tai1 TAI as a 2-part Julian Date (Note 1)
19963 * @param tai2 TAI as a 2-part Julian Date (Note 1)
19964 *
19965 *<!-- Returned:-->
19966 * @return UTC as a 2-part quasi Julian Date (Notes 1-3)
19967 *
19968 * Returned (function value):
19969 * int status: +1 = dubious year (Note 4)
19970 * 0 = OK
19971 * -1 = unacceptable date
19972 *
19973 *<p>Notes:</p>
19974 * <ol>
19975 * <li> tai1+tai2 is Julian Date, apportioned in any convenient way
19976 * between the two arguments, for example where tai1 is the Julian
19977 * Day Number and tai2 is the fraction of a day. The returned utc1
19978 * and utc2 form an analogous pair, except that a special convention
19979 * is used, to deal with the problem of leap seconds - see the next
19980 * note.
19981 *
19982 * <li> JD cannot unambiguously represent UTC during a leap second unless
19983 * special measures are taken. The convention in the present
19984 * function is that the JD day represents UTC days whether the
19985 * length is 86399, 86400 or 86401 SI seconds.
19986 *
19987 * <li> The function jauD2dtf can be used to transform the UTC quasi-JD
19988 * into calendar date and clock time, including UTC leap second
19989 * handling.
19990 *
19991 * <li> The warning status "dubious year" flags UTCs that predate the
19992 * introduction of the time scale and that are too far in the future
19993 * to be trusted. See jauDat for further details.
19994 * </ol>
19995 * Called:
19996 * <ul>
19997 * <li>{@link #jauJd2cal} JD to Gregorian calendar
19998 * <li>{@link #jauDat} delta(AT) = TAI-UTC
19999 * <li>{@link #jauCal2jd} Gregorian calendar to JD
20000 *</ul>
20001 *<p>References:
20002 *
20003 * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
20004 * IERS Technical Note No. 32, BKG (2004)
20005 *
20006 * Explanatory Supplement to the Astronomical Almanac,
20007 * P. Kenneth Seidelmann (ed), University Science Books (1992)
20008 *
20009 *@version 2010 May 16
20010 *
20011 *@since SOFA release 2010-12-01
20012 *
20013 * <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
20014 * @throws JSOFAIllegalParameter
20015 * @throws JSOFAInternalError
20016 */
20017 public static JulianDate jauTaiutc(double tai1, double tai2) throws JSOFAIllegalParameter, JSOFAInternalError
20018 {
20019 boolean big1;
20020 int i;
20021 double a1, a2,dats1, ddats, dats2, datd = 0.0, as1, as2, da, d1, d2, fd;
20022 double utc1, utc2;
20023
20024
20025 /* Put the two parts of the TAI into big-first order. */
20026 big1 = ( tai1 >= tai2 );
20027 if ( big1 ) {
20028 a1 = tai1;
20029 a2 = tai2;
20030 } else {
20031 a1 = tai2;
20032 a2 = tai1;
20033 }
20034
20035 /* See if the TAI can possibly be in a leap-second day. */
20036 d1 = a1;
20037 dats1 = 0.0;
20038 for ( i = -1; i <= 3; i++ ) {
20039 d2 = a2 + (double) i;
20040 Calendar dt;
20041 dt = jauJd2cal(d1, d2 );
20042 dats2 = jauDat(dt.iy, dt.im, dt.id, 0.0);
20043 //FIXME if ( js < 0 ) return -1;
20044 if ( i == -1 ) dats1 = dats2;
20045 ddats = dats2 - dats1;
20046 datd = dats1 / DAYSEC;
20047 if ( abs(ddats) >= 0.5 ) {
20048
20049 /* Yes. Get TAI for the start of the UTC day that */
20050 /* ends in a leap. */
20051 JulianDate jd = jauCal2jd(dt.iy, dt.im, dt.id );
20052 d1 = jd.djm0; d2 = jd.djm1;
20053 as1 = d1;
20054 as2 = d2 - 1.0 + datd;
20055
20056 /* Is the TAI after this point? */
20057 da = a1 - as1;
20058 da = da + ( a2 - as2 );
20059 if ( da > 0 ) {
20060
20061 /* Yes: fraction of the current UTC day that has elapsed. */
20062 fd = da * DAYSEC / ( DAYSEC + ddats );
20063
20064 /* Ramp TAI-UTC to bring about SOFA's JD(UTC) convention. */
20065 datd += ddats * ( fd <= 1.0 ? fd : 1.0 ) / DAYSEC;
20066 }
20067
20068 /* Done. */
20069 break;
20070 }
20071 dats1 = dats2;
20072 }
20073
20074 /* Subtract the (possibly adjusted) TAI-UTC from TAI to give UTC. */
20075 a2 -= datd;
20076
20077 /* Return the UTC result, preserving the TAI order. */
20078 if ( big1 ) {
20079 utc1 = a1;
20080 utc2 = a2;
20081 } else {
20082 utc1 = a2;
20083 utc2 = a1;
20084 }
20085
20086 /* TODO Status */
20087 return new JulianDate(utc1, utc2);
20088
20089 };
20090
20091 /**
20092 *
20093 * Time scale transformation: Barycentric Coordinate Time, TCB, to
20094 * Barycentric Dynamical Time, TDB.
20095 *
20096 * <p>This function is derived from the International Astronomical Union's
20097 * SOFA (Standards of Fundamental Astronomy) software collection.
20098 *
20099 *<p>Status: canonical.
20100 *
20101 *<!-- Given: -->
20102 * @param tcb1 double TCB as a 2-part Julian Date
20103 * @param tcb2 double TCB as a 2-part Julian Date
20104 *
20105 *<!-- Returned:-->
20106 * @return TDB as a 2-part Julian Date
20107 *
20108 *
20109 *<p>Notes:
20110 * <ol>
20111 * <li> tcb1+tcb2 is Julian Date, apportioned in any convenient way
20112 * between the two arguments, for example where tcb1 is the Julian
20113 * Day Number and tcb2 is the fraction of a day. The returned
20114 * tdb1,tdb2 follow suit.
20115 *
20116 * <li> The 2006 IAU General Assembly introduced a conventional linear
20117 * transformation between TDB and TCB. This transformation
20118 * compensates for the drift between TCB and terrestrial time TT,
20119 * and keeps TDB approximately centered on TT. Because the
20120 * relationship between TT and TCB depends on the adopted solar
20121 * system ephemeris, the degree of alignment between TDB and TT over
20122 * long intervals will vary according to which ephemeris is used.
20123 * Former definitions of TDB attempted to avoid this problem by
20124 * stipulating that TDB and TT should differ only by periodic
20125 * effects. This is a good description of the nature of the
20126 * relationship but eluded precise mathematical formulation. The
20127 * conventional linear relationship adopted in 2006 sidestepped
20128 * these difficulties whilst delivering a TDB that in practice was
20129 * consistent with values before that date.
20130 *
20131 * <li> TDB is essentially the same as Teph, the time argument for the
20132 * JPL solar system ephemerides.
20133 * </ol>
20134 * Reference:
20135 *
20136 * IAU 2006 Resolution B3
20137 *
20138 *@version 2010 May 16
20139 *
20140 *@since SOFA release 2010-12-01
20141 *
20142 * <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
20143 */
20144 public static JulianDate jauTcbtdb(double tcb1, double tcb2)
20145 {
20146 double tdb1, tdb2;
20147 /* 1977 Jan 1 00:00:32.184 TT, as two-part JD */
20148 final double t77td = DJM0 + DJM77;
20149 final double t77tf = TTMTAI/DAYSEC;
20150
20151 /* TDB (days) at TAI 1977 Jan 1.0 */
20152 final double tdb0 = TDB0/86400.0;
20153
20154 double d;
20155
20156
20157 /* Result, safeguarding precision. */
20158 if ( tcb1 > tcb2 ) {
20159 d = tcb1 - t77td;
20160 tdb1 = tcb1;
20161 tdb2 = tcb2 + tdb0 - ( d + ( tcb2 - t77tf ) ) * ELB;
20162 } else {
20163 d = tcb2 - t77td;
20164 tdb1 = tcb1 + tdb0 - ( d + ( tcb1 - t77tf ) ) * ELB;
20165 tdb2 = tcb2;
20166 }
20167
20168
20169 return new JulianDate(tdb1, tdb2);
20170
20171 };
20172
20173 /**
20174 * Time scale transformation: Geocentric Coordinate Time, TCG, to
20175 * Terrestrial Time, TT.
20176 *
20177 * <p>This function is derived from the International Astronomical Union's
20178 * SOFA (Standards of Fundamental Astronomy) software collection.
20179 *
20180 *<p>Status: canonical.
20181 *
20182 *<!-- Given: -->
20183 * @param tcg1 double TCG as a 2-part Julian Date
20184 * @param tcg2 double TCG as a 2-part Julian Date
20185 *
20186 *<!-- Returned:-->
20187 * @return TT as a 2-part Julian Date
20188 *
20189 *
20190 * Note:
20191 *
20192 * tcg1+tcg2 is Julian Date, apportioned in any convenient way
20193 * between the two arguments, for example where tcg1 is the Julian
20194 * Day Number and tcg22 is the fraction of a day. The returned
20195 * tt1,tt2 follow suit.
20196 *
20197 *<p>References:
20198 *
20199 * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),.
20200 * IERS Technical Note No. 32, BKG (2004)
20201 *
20202 * IAU 2000 Resolution B1.9
20203 *
20204 *@version 2010 May 14
20205 *
20206 *@since SOFA release 2010-12-01
20207 *
20208 * <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
20209 */
20210 public static JulianDate jauTcgtt(double tcg1, double tcg2)
20211 {
20212 double tt1,tt2;
20213 /* 1977 Jan 1 00:00:32.184 TT, as MJD */
20214 final double t77t = DJM77 + TTMTAI/DAYSEC;
20215
20216
20217 /* Result, safeguarding precision. */
20218 if ( tcg1 > tcg2 ) {
20219 tt1 = tcg1;
20220 tt2 = tcg2 - ( ( tcg1 - DJM0 ) + ( tcg2 - t77t ) ) * ELG;
20221 } else {
20222 tt1 = tcg1 - ( ( tcg2 - DJM0 ) + ( tcg1 - t77t ) ) * ELG;
20223 tt2 = tcg2;
20224 }
20225
20226 return new JulianDate(tt1, tt2);
20227 };
20228
20229
20230 /**
20231 *
20232 * Time scale transformation: Barycentric Dynamical Time, TDB, to
20233 * Barycentric Coordinate Time, TCB.
20234 *
20235 * <p>This function is derived from the International Astronomical Union's
20236 * SOFA (Standards of Fundamental Astronomy) software collection.
20237 *
20238 *<p>Status: canonical.
20239 *
20240 *<!-- Given: -->
20241 * @param tdb1 TDB as a 2-part Julian Date
20242 * @param tdb2 TDB as a 2-part Julian Date
20243 *
20244 *<!-- Returned:-->
20245 * @return TCB as a 2-part Julian Date
20246 *
20247 *<p>Notes:
20248 * <ol>
20249 * <li> tdb1+tdb2 is Julian Date, apportioned in any convenient way
20250 * between the two arguments, for example where tdb1 is the Julian
20251 * Day Number and tdb2 is the fraction of a day. The returned
20252 * tcb1,tcb2 follow suit.
20253 *
20254 * <li> The 2006 IAU General Assembly introduced a conventional linear
20255 * transformation between TDB and TCB. This transformation
20256 * compensates for the drift between TCB and terrestrial time TT,
20257 * and keeps TDB approximately centered on TT. Because the
20258 * relationship between TT and TCB depends on the adopted solar
20259 * system ephemeris, the degree of alignment between TDB and TT over
20260 * long intervals will vary according to which ephemeris is used.
20261 * Former definitions of TDB attempted to avoid this problem by
20262 * stipulating that TDB and TT should differ only by periodic
20263 * effects. This is a good description of the nature of the
20264 * relationship but eluded precise mathematical formulation. The
20265 * conventional linear relationship adopted in 2006 sidestepped
20266 * these difficulties whilst delivering a TDB that in practice was
20267 * consistent with values before that date.
20268 *
20269 * <li> TDB is essentially the same as Teph, the time argument for the
20270 * JPL solar system ephemerides.
20271 * </ol>
20272 * Reference:
20273 *
20274 * IAU 2006 Resolution B3
20275 *
20276 *@version 2010 September 10
20277 *
20278 *@since SOFA release 2010-12-01
20279 *
20280 * <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
20281 */
20282 public static JulianDate jauTdbtcb(double tdb1, double tdb2 )
20283 {
20284 double tcb1, tcb2;
20285 /* 1977 Jan 1 00:00:32.184 TT, as two-part JD */
20286 final double t77td = DJM0 + DJM77;
20287 final double t77tf = TTMTAI/DAYSEC;
20288
20289 /* TDB (days) at TAI 1977 Jan 1.0 */
20290 final double tdb0 = TDB0/DAYSEC;
20291
20292 /* TDB to TCB rate */
20293 final double elbb = ELB/(1.0-ELB);
20294
20295 double d, f;
20296
20297
20298 /* Result, preserving date format but safeguarding precision. */
20299 if ( tdb1 > tdb2 ) {
20300 d = t77td - tdb1;
20301 f = tdb2 - tdb0;
20302 tcb1 = tdb1;
20303 tcb2 = f - ( d - ( f - t77tf ) ) * elbb;
20304 } else {
20305 d = t77td - tdb2;
20306 f = tdb1 - tdb0;
20307 tcb1 = f + ( d - ( f - t77tf ) ) * elbb;
20308 tcb2 = tdb2;
20309 }
20310
20311 return new JulianDate(tcb1, tcb2);
20312
20313 };
20314
20315
20316 /**
20317 *
20318 * Time scale transformation: Barycentric Dynamical Time, TDB, to
20319 * Terrestrial Time, TT.
20320 *
20321 * <p>This function is derived from the International Astronomical Union's
20322 * SOFA (Standards of Fundamental Astronomy) software collection.
20323 *
20324 *<p>Status: canonical.
20325 *
20326 *<!-- Given: -->
20327 * @param tdb1 double TDB as a 2-part Julian Date
20328 * @param tdb2 double TDB as a 2-part Julian Date
20329 * @param dtr double TDB-TT in seconds
20330 *
20331 *<!-- Returned:-->
20332 * @return TT as a 2-part Julian Date
20333 *
20334 *
20335 *<p>Notes:
20336 * <ol>
20337 * <li> tdb1+tdb2 is Julian Date, apportioned in any convenient way
20338 * between the two arguments, for example where tdb1 is the Julian
20339 * Day Number and tdb2 is the fraction of a day. The returned
20340 * tt1,tt2 follow suit.
20341 *
20342 * <li> The argument dtr represents the quasi-periodic component of the
20343 * GR transformation between TT and TCB. It is dependent upon the
20344 * adopted solar-system ephemeris, and can be obtained by numerical
20345 * integration, by interrogating a precomputed time ephemeris or by
20346 * evaluating a model such as that implemented in the SOFA function
20347 * jauDtdb. The quantity is dominated by an annual term of 1.7 ms
20348 * amplitude.
20349 *
20350 * <li> TDB is essentially the same as Teph, the time argument for the
20351 * JPL solar system ephemerides.
20352 * </ol>
20353 *<p>References:
20354 *
20355 * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
20356 * IERS Technical Note No. 32, BKG (2004)
20357 *
20358 * IAU 2006 Resolution 3
20359 *
20360 *@version 2010 May 13
20361 *
20362 *@since SOFA release 2010-12-01
20363 *
20364 * <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
20365 *
20366 */
20367 public static JulianDate jauTdbtt(double tdb1, double tdb2, double dtr )
20368 {
20369 double tt1, tt2;
20370 double dtrd;
20371
20372
20373 /* Result, safeguarding precision. */
20374 dtrd = dtr / DAYSEC;
20375 if ( tdb1 > tdb2 ) {
20376 tt1 = tdb1;
20377 tt2 = tdb2 - dtrd;
20378 } else {
20379 tt1 = tdb1 - dtrd;
20380 tt2 = tdb2;
20381 }
20382
20383 return new JulianDate(tt1, tt2);
20384
20385 }
20386
20387 /**
20388 *
20389 * Convert hours, minutes, seconds to radians.
20390 *
20391 * <p>This function is derived from the International Astronomical Union's
20392 * SOFA (Standards of Fundamental Astronomy) software collection.
20393 *
20394 *<p>Status: support function.
20395 *
20396 *<!-- Given: -->
20397 * @param s char sign: '-' = negative, otherwise positive
20398 * @param ihour int hours
20399 * @param imin int minutes
20400 * @param sec double seconds
20401 *
20402 *<!-- Returned:-->
20403 * @return double angle in radians
20404 *@throws JSOFAIllegalParameter illegal parameter of some form
20405 * Returned (function value):
20406 * int status: 0 = OK
20407 * 1 = ihour outside range 0-23
20408 * 2 = imin outside range 0-59
20409 * 3 = sec outside range 0-59.999...
20410 *
20411 *<p>Notes:
20412 *<ul>
20413 * <li> The result is computed even if any of the range checks fail.
20414 *
20415 * <li> Negative ihour, imin and/or sec produce a warning status, but
20416 * the absolute value is used in the conversion.
20417 *</ul>
20418 *@version 2010 August 27
20419 *
20420 *@since SOFA release 2010-12-01
20421 *
20422 * <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
20423 *
20424 */
20425 public static double jauTf2a(char s, int ihour, int imin, double sec ) throws JSOFAIllegalParameter
20426 {
20427 double rad;
20428
20429 /* Compute the interval. */
20430 rad = ( s == '-' ? -1.0 : 1.0 ) *
20431 ( 60.0 * ( 60.0 * ( (double) abs(ihour) ) +
20432 ( (double) abs(imin) ) ) +
20433 abs(sec) ) * DS2R;
20434
20435 /* Validate arguments and return status. */
20436 if ( ihour < 0 || ihour > 23 ) throw new JSOFAIllegalParameter("bad hour", 1);
20437 if ( imin < 0 || imin > 59 ) throw new JSOFAIllegalParameter("bad minute", 2);
20438 if ( sec < 0.0 || sec >= 60.0 )throw new JSOFAIllegalParameter("bad second", 3);
20439 return rad;
20440
20441 };
20442
20443 /**
20444 *
20445 * Convert hours, minutes, seconds to days.
20446 *
20447 * <p>This function is derived from the International Astronomical Union's
20448 * SOFA (Standards of Fundamental Astronomy) software collection.
20449 *
20450 *<p>Status: support function.
20451 *
20452 *<!-- Given: -->
20453 * @param s char sign: '-' = negative, otherwise positive
20454 * @param ihour int hours
20455 * @param imin int minutes
20456 * @param sec double seconds
20457 *
20458 *<!-- Returned:-->
20459 * days double interval in days
20460 *
20461 * Returned (function value):
20462 * int status: 0 = OK
20463 * 1 = ihour outside range 0-23
20464 * 2 = imin outside range 0-59
20465 * 3 = sec outside range 0-59.999...
20466 *
20467 *<p>Notes:
20468 *<ol>
20469 * <li> The result is computed even if any of the range checks fail.
20470 *
20471 * <li> Negative ihour, imin and/or sec produce a warning status, but
20472 * the absolute value is used in the conversion.
20473 *</ol>
20474 *@version 2010 August 27
20475 *
20476 *@since SOFA release 2010-12-01
20477 *
20478 * <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
20479 * @throws JSOFAIllegalParameter
20480 */
20481 public static double jauTf2d(char s, int ihour, int imin, double sec) throws JSOFAIllegalParameter
20482 {
20483 double days;
20484 /* Compute the interval. */
20485 days = ( s == '-' ? -1.0 : 1.0 ) *
20486 ( 60.0 * ( 60.0 * ( (double) abs(ihour) ) +
20487 ( (double) abs(imin) ) ) +
20488 abs(sec) ) / DAYSEC;
20489
20490 /* FIXME Validate arguments and return status. */
20491 if ( ihour < 0 || ihour > 23 ) throw new JSOFAIllegalParameter("bad hour", 1);
20492 if ( imin < 0 || imin > 59 ) throw new JSOFAIllegalParameter("bad minute", 2);
20493 if ( sec < 0.0 || sec >= 60.0 ) throw new JSOFAIllegalParameter("bad second", 3);
20494 return days;
20495
20496 }
20497
20498 /**
20499 * Transpose an r-matrix.
20500 *
20501 *<p>This function is derived from the International Astronomical Union's
20502 * SOFA (Standards Of Fundamental Astronomy) software collection.
20503 *
20504 *<p>Status: vector/matrix support function.
20505 *
20506 *<!-- Given: -->
20507 * @param r double[3][3] r-matrix
20508 *
20509 *<!-- Returned: -->
20510 * @return rt double[3][3] <u>returned</u> transpose
20511 *
20512 * Note:
20513 * It is permissible for r and rt to be the same array.
20514 *
20515 *<p>Called:<ul>
20516 * <li>{@link #jauCr} copy r-matrix
20517 * </ul>
20518 *@version 2008 May 22
20519 *
20520 * @since Release 20101201
20521 *
20522 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
20523 */
20524 public static double[][] jauTr(double r[][])
20525 {
20526 double wm[][]= new double[3][3];
20527 int i, j;
20528
20529
20530 for (i = 0; i < 3; i++) {
20531 for (j = 0; j < 3; j++) {
20532 wm[i][j] = r[j][i];
20533 }
20534 }
20535
20536
20537 return wm;
20538
20539 }
20540
20541
20542 /**
20543 * Multiply a p-vector by the transpose of an r-matrix.
20544 *
20545 *<p>This function is derived from the International Astronomical Union's
20546 * SOFA (Standards Of Fundamental Astronomy) software collection.
20547 *
20548 *<p>Status: vector/matrix support function.
20549 *
20550 *<!-- Given: -->
20551 * @param r double[3][3] r-matrix
20552 * @param p double[3] p-vector
20553 *
20554 *<!-- Returned: -->
20555 * @return trp double[3] <u>returned</u> r * p
20556 *
20557 * Note:
20558 * It is permissible for p and trp to be the same array.
20559 *
20560 *<p>Called:<ul>
20561 * <li>{@link #jauTr} transpose r-matrix
20562 * <li>{@link #jauRxp} product of r-matrix and p-vector
20563 * </ul>
20564 *@version 2008 October 28
20565 *
20566 * @since Release 20101201
20567 *
20568 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
20569 */
20570 public static double[] jauTrxp(double r[][], double p[] )
20571 {
20572 double tr[][];
20573 double trp[];
20574
20575 /* Transpose of matrix r. */
20576 tr = jauTr(r);
20577
20578 /* Matrix tr * vector p -> vector trp. */
20579 trp = jauRxp(tr, p);
20580
20581 return trp;
20582
20583 }
20584
20585
20586 /**
20587 * Multiply a pv-vector by the transpose of an r-matrix.
20588 *
20589 *<p>This function is derived from the International Astronomical Union's
20590 * SOFA (Standards Of Fundamental Astronomy) software collection.
20591 *
20592 *<p>Status: vector/matrix support function.
20593 *
20594 *<!-- Given: -->
20595 * @param r double[3][3] r-matrix
20596 * @param pv double[2][3] pv-vector
20597 *
20598 *<!-- Returned: -->
20599 * @return trpv double[2][3] <u>returned</u> r * pv
20600 *
20601 * Note:
20602 * It is permissible for pv and trpv to be the same array.
20603 *
20604 *<p>Called:<ul>
20605 * <li>{@link #jauTr} transpose r-matrix
20606 * <li>{@link #jauRxpv} product of r-matrix and pv-vector
20607 * </ul>
20608 *@version 2008 October 28
20609 *
20610 * @since Release 20101201
20611 *
20612 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
20613 */
20614 public static double[][] jauTrxpv(double r[][], double pv[][] )
20615 {
20616 double tr[][], trpv[][];
20617
20618
20619 /* Transpose of matrix r. */
20620 tr = jauTr(r);
20621
20622 /* Matrix tr * vector pv -> vector trpv. */
20623 trpv = jauRxpv(tr, pv);
20624
20625 return trpv;
20626
20627 }
20628
20629 /*
20630 * constant arrays set outside jauXy06 to avoid problems with 65535 byte limit on function size
20631 */
20632 static {
20633 /* need to define this function because it appears that javac lumps all of the statically defined initalizers into one function on
20634 * compilation - so this will force a second function */
20635 init_mfals();
20636 }
20637 /** Fundamental-argument multipliers: luni-solar terms */
20638 private static int mfals[][]; //IMPL would like to be final really
20639
20640 private static void init_mfals(){
20641
20642 mfals = new int[][]
20643 {
20644
20645 /* 1-10 */
20646 { 0, 0, 0, 0, 1 },
20647 { 0, 0, 2, -2, 2 },
20648 { 0, 0, 2, 0, 2 },
20649 { 0, 0, 0, 0, 2 },
20650 { 0, 1, 0, 0, 0 },
20651 { 0, 1, 2, -2, 2 },
20652 { 1, 0, 0, 0, 0 },
20653 { 0, 0, 2, 0, 1 },
20654 { 1, 0, 2, 0, 2 },
20655 { 0, 1, -2, 2, -2 },
20656
20657 /* 11-20 */
20658 { 0, 0, 2, -2, 1 },
20659 { 1, 0, -2, 0, -2 },
20660 { 1, 0, 0, -2, 0 },
20661 { 1, 0, 0, 0, 1 },
20662 { 1, 0, 0, 0, -1 },
20663 { 1, 0, -2, -2, -2 },
20664 { 1, 0, 2, 0, 1 },
20665 { 2, 0, -2, 0, -1 },
20666 { 0, 0, 0, 2, 0 },
20667 { 0, 0, 2, 2, 2 },
20668
20669 /* 21-30 */
20670 { 2, 0, 0, -2, 0 },
20671 { 0, 2, -2, 2, -2 },
20672 { 2, 0, 2, 0, 2 },
20673 { 1, 0, 2, -2, 2 },
20674 { 1, 0, -2, 0, -1 },
20675 { 2, 0, 0, 0, 0 },
20676 { 0, 0, 2, 0, 0 },
20677 { 0, 1, 0, 0, 1 },
20678 { 1, 0, 0, -2, -1 },
20679 { 0, 2, 2, -2, 2 },
20680
20681 /* 31-40 */
20682 { 0, 0, 2, -2, 0 },
20683 { 1, 0, 0, -2, 1 },
20684 { 0, 1, 0, 0, -1 },
20685 { 0, 2, 0, 0, 0 },
20686 { 1, 0, -2, -2, -1 },
20687 { 1, 0, 2, 2, 2 },
20688 { 0, 1, 2, 0, 2 },
20689 { 2, 0, -2, 0, 0 },
20690 { 0, 0, 2, 2, 1 },
20691 { 0, 1, -2, 0, -2 },
20692
20693 /* 41-50 */
20694 { 0, 0, 0, 2, 1 },
20695 { 1, 0, 2, -2, 1 },
20696 { 2, 0, 0, -2, -1 },
20697 { 2, 0, 2, -2, 2 },
20698 { 2, 0, 2, 0, 1 },
20699 { 0, 0, 0, 2, -1 },
20700 { 0, 1, -2, 2, -1 },
20701 { 1, 1, 0, -2, 0 },
20702 { 2, 0, 0, -2, 1 },
20703 { 1, 0, 0, 2, 0 },
20704
20705 /* 51-60 */
20706 { 0, 1, 2, -2, 1 },
20707 { 1, -1, 0, 0, 0 },
20708 { 0, 1, -1, 1, -1 },
20709 { 2, 0, -2, 0, -2 },
20710 { 0, 1, 0, -2, 0 },
20711 { 1, 0, 0, -1, 0 },
20712 { 3, 0, 2, 0, 2 },
20713 { 0, 0, 0, 1, 0 },
20714 { 1, -1, 2, 0, 2 },
20715 { 1, 1, -2, -2, -2 },
20716
20717 /* 61-70 */
20718 { 1, 0, -2, 0, 0 },
20719 { 2, 0, 0, 0, -1 },
20720 { 0, 1, -2, -2, -2 },
20721 { 1, 1, 2, 0, 2 },
20722 { 2, 0, 0, 0, 1 },
20723 { 1, 1, 0, 0, 0 },
20724 { 1, 0, -2, 2, -1 },
20725 { 1, 0, 2, 0, 0 },
20726 { 1, -1, 0, -1, 0 },
20727 { 1, 0, 0, 0, 2 },
20728
20729 /* 71-80 */
20730 { 1, 0, -1, 0, -1 },
20731 { 0, 0, 2, 1, 2 },
20732 { 1, 0, -2, -4, -2 },
20733 { 1, -1, 0, -1, -1 },
20734 { 1, 0, 2, 2, 1 },
20735 { 0, 2, -2, 2, -1 },
20736 { 1, 0, 0, 0, -2 },
20737 { 2, 0, -2, -2, -2 },
20738 { 1, 1, 2, -2, 2 },
20739 { 2, 0, -2, -4, -2 },
20740
20741 /* 81-90 */
20742 { 1, 0, -4, 0, -2 },
20743 { 2, 0, 2, -2, 1 },
20744 { 1, 0, 0, -1, -1 },
20745 { 2, 0, 2, 2, 2 },
20746 { 3, 0, 0, 0, 0 },
20747 { 1, 0, 0, 2, 1 },
20748 { 0, 0, 2, -2, -1 },
20749 { 3, 0, 2, -2, 2 },
20750 { 0, 0, 4, -2, 2 },
20751 { 1, 0, 0, -4, 0 },
20752
20753 /* 91-100 */
20754 { 0, 1, 2, 0, 1 },
20755 { 2, 0, 0, -4, 0 },
20756 { 1, 1, 0, -2, -1 },
20757 { 2, 0, -2, 0, 1 },
20758 { 0, 0, 2, 0, -1 },
20759 { 0, 1, -2, 0, -1 },
20760 { 0, 1, 0, 0, 2 },
20761 { 0, 0, 2, -1, 2 },
20762 { 0, 0, 2, 4, 2 },
20763 { 2, 1, 0, -2, 0 },
20764
20765 /* 101-110 */
20766 { 1, 1, 0, -2, 1 },
20767 { 1, -1, 0, -2, 0 },
20768 { 1, -1, 0, -1, -2 },
20769 { 1, -1, 0, 0, 1 },
20770 { 0, 1, -2, 2, 0 },
20771 { 0, 1, 0, 0, -2 },
20772 { 1, -1, 2, 2, 2 },
20773 { 1, 0, 0, 2, -1 },
20774 { 1, -1, -2, -2, -2 },
20775 { 3, 0, 2, 0, 1 },
20776
20777 /* 111-120 */
20778 { 0, 1, 2, 2, 2 },
20779 { 1, 0, 2, -2, 0 },
20780 { 1, 1, -2, -2, -1 },
20781 { 1, 0, 2, -4, 1 },
20782 { 0, 1, -2, -2, -1 },
20783 { 2, -1, 2, 0, 2 },
20784 { 0, 0, 0, 2, 2 },
20785 { 1, -1, 2, 0, 1 },
20786 { 1, -1, -2, 0, -2 },
20787 { 0, 1, 0, 2, 0 },
20788
20789 /* 121-130 */
20790 { 0, 1, 2, -2, 0 },
20791 { 0, 0, 0, 1, 1 },
20792 { 1, 0, -2, -2, 0 },
20793 { 0, 3, 2, -2, 2 },
20794 { 2, 1, 2, 0, 2 },
20795 { 1, 1, 0, 0, 1 },
20796 { 2, 0, 0, 2, 0 },
20797 { 1, 1, 2, 0, 1 },
20798 { 1, 0, 0, -2, -2 },
20799 { 1, 0, -2, 2, 0 },
20800
20801 /* 131-140 */
20802 { 1, 0, -1, 0, -2 },
20803 { 0, 1, 0, -2, 1 },
20804 { 0, 1, 0, 1, 0 },
20805 { 0, 0, 0, 1, -1 },
20806 { 1, 0, -2, 2, -2 },
20807 { 1, -1, 0, 0, -1 },
20808 { 0, 0, 0, 4, 0 },
20809 { 1, -1, 0, 2, 0 },
20810 { 1, 0, 2, 1, 2 },
20811 { 1, 0, 2, -1, 2 },
20812
20813 /* 141-150 */
20814 { 0, 0, 2, 1, 1 },
20815 { 1, 0, 0, -2, 2 },
20816 { 1, 0, -2, 0, 1 },
20817 { 1, 0, -2, -4, -1 },
20818 { 0, 0, 2, 2, 0 },
20819 { 1, 1, 2, -2, 1 },
20820 { 1, 0, -2, 1, -1 },
20821 { 0, 0, 1, 0, 1 },
20822 { 2, 0, -2, -2, -1 },
20823 { 4, 0, 2, 0, 2 },
20824
20825 /* 151-160 */
20826 { 2, -1, 0, 0, 0 },
20827 { 2, 1, 2, -2, 2 },
20828 { 0, 1, 2, 1, 2 },
20829 { 1, 0, 4, -2, 2 },
20830 { 1, 1, 0, 0, -1 },
20831 { 2, 0, 2, 0, 0 },
20832 { 2, 0, -2, -4, -1 },
20833 { 1, 0, -1, 0, 0 },
20834 { 1, 0, 0, 1, 0 },
20835 { 0, 1, 0, 2, 1 },
20836
20837 /* 161-170 */
20838 { 1, 0, -4, 0, -1 },
20839 { 1, 0, 0, -4, -1 },
20840 { 2, 0, 2, 2, 1 },
20841 { 2, 1, 0, 0, 0 },
20842 { 0, 0, 2, -3, 2 },
20843 { 1, 2, 0, -2, 0 },
20844 { 0, 3, 0, 0, 0 },
20845 { 0, 0, 4, 0, 2 },
20846 { 0, 0, 2, -4, 1 },
20847 { 2, 0, 0, -2, -2 },
20848
20849 /* 171-180 */
20850 { 1, 1, -2, -4, -2 },
20851 { 0, 1, 0, -2, -1 },
20852 { 0, 0, 0, 4, 1 },
20853 { 3, 0, 2, -2, 1 },
20854 { 1, 0, 2, 4, 2 },
20855 { 1, 1, -2, 0, -2 },
20856 { 0, 0, 4, -2, 1 },
20857 { 2, -2, 0, -2, 0 },
20858 { 2, 1, 0, -2, -1 },
20859 { 0, 2, 0, -2, 0 },
20860
20861 /* 181-190 */
20862 { 1, 0, 0, -1, 1 },
20863 { 1, 1, 2, 2, 2 },
20864 { 3, 0, 0, 0, -1 },
20865 { 2, 0, 0, -4, -1 },
20866 { 3, 0, 2, 2, 2 },
20867 { 0, 0, 2, 4, 1 },
20868 { 0, 2, -2, -2, -2 },
20869 { 1, -1, 0, -2, -1 },
20870 { 0, 0, 2, -1, 1 },
20871 { 2, 0, 0, 2, 1 },
20872
20873 /* 191-200 */
20874 { 1, -1, -2, 2, -1 },
20875 { 0, 0, 0, 2, -2 },
20876 { 2, 0, 0, -4, 1 },
20877 { 1, 0, 0, -4, 1 },
20878 { 2, 0, 2, -4, 1 },
20879 { 4, 0, 2, -2, 2 },
20880 { 2, 1, -2, 0, -1 },
20881 { 2, 1, -2, -4, -2 },
20882 { 3, 0, 0, -4, 0 },
20883 { 1, -1, 2, 2, 1 },
20884
20885 /* 201-210 */
20886 { 1, -1, -2, 0, -1 },
20887 { 0, 2, 0, 0, 1 },
20888 { 1, 2, -2, -2, -2 },
20889 { 1, 1, 0, -4, 0 },
20890 { 2, 0, 0, -2, 2 },
20891 { 0, 2, 2, -2, 1 },
20892 { 1, 0, 2, 0, -1 },
20893 { 2, 1, 0, -2, 1 },
20894 { 2, -1, -2, 0, -1 },
20895 { 1, -1, -2, -2, -1 },
20896
20897 /* 211-220 */
20898 { 0, 1, -2, 1, -2 },
20899 { 1, 0, -4, 2, -2 },
20900 { 0, 1, 2, 2, 1 },
20901 { 3, 0, 0, 0, 1 },
20902 { 2, -1, 2, 2, 2 },
20903 { 0, 1, -2, -4, -2 },
20904 { 1, 0, -2, -3, -2 },
20905 { 2, 0, 0, 0, 2 },
20906 { 1, -1, 0, -2, -2 },
20907 { 2, 0, -2, 2, -1 },
20908
20909 /* 221-230 */
20910 { 0, 2, -2, 0, -2 },
20911 { 3, 0, -2, 0, -1 },
20912 { 2, -1, 2, 0, 1 },
20913 { 1, 0, -2, -1, -2 },
20914 { 0, 0, 2, 0, 3 },
20915 { 2, 0, -4, 0, -2 },
20916 { 2, 1, 0, -4, 0 },
20917 { 1, 1, -2, 1, -1 },
20918 { 0, 2, 2, 0, 2 },
20919 { 1, -1, 2, -2, 2 },
20920
20921 /* 231-240 */
20922 { 1, -1, 0, -2, 1 },
20923 { 2, 1, 2, 0, 1 },
20924 { 1, 0, 2, -4, 2 },
20925 { 1, 1, -2, 0, -1 },
20926 { 1, 1, 0, 2, 0 },
20927 { 1, 0, 0, -3, 0 },
20928 { 2, 0, 2, -1, 2 },
20929 { 0, 2, 0, 0, -1 },
20930 { 2, -1, 0, -2, 0 },
20931 { 4, 0, 0, 0, 0 },
20932
20933 /* 241-250 */
20934 { 2, 1, -2, -2, -2 },
20935 { 0, 2, -2, 2, 0 },
20936 { 1, 0, 2, 1, 1 },
20937 { 1, 0, -1, 0, -3 },
20938 { 3, -1, 2, 0, 2 },
20939 { 2, 0, 2, -2, 0 },
20940 { 1, -2, 0, 0, 0 },
20941 { 2, 0, 0, 0, -2 },
20942 { 1, 0, 0, 4, 0 },
20943 { 0, 1, 0, 1, 1 },
20944
20945 /* 251-260 */
20946 { 1, 0, 2, 2, 0 },
20947 { 0, 1, 0, 2, -1 },
20948 { 0, 1, 0, 1, -1 },
20949 { 0, 0, 2, -2, 3 },
20950 { 3, 1, 2, 0, 2 },
20951 { 1, 1, 2, 1, 2 },
20952 { 1, 1, -2, 2, -1 },
20953 { 2, -1, 2, -2, 2 },
20954 { 1, -2, 2, 0, 2 },
20955 { 1, 0, 2, -4, 0 },
20956
20957 /* 261-270 */
20958 { 0, 0, 1, 0, 0 },
20959 { 1, 0, 2, -3, 1 },
20960 { 1, -2, 0, -2, 0 },
20961 { 2, 0, 0, 2, -1 },
20962 { 1, 1, 2, -4, 1 },
20963 { 4, 0, 2, 0, 1 },
20964 { 0, 1, 2, 1, 1 },
20965 { 1, 2, 2, -2, 2 },
20966 { 2, 0, 2, 1, 2 },
20967 { 2, 1, 2, -2, 1 },
20968
20969 /* 271-280 */
20970 { 1, 0, 2, -1, 1 },
20971 { 1, 0, 4, -2, 1 },
20972 { 1, -1, 2, -2, 1 },
20973 { 0, 1, 0, -4, 0 },
20974 { 3, 0, -2, -2, -2 },
20975 { 0, 0, 4, -4, 2 },
20976 { 2, 0, -4, -2, -2 },
20977 { 2, -2, 0, -2, -1 },
20978 { 1, 0, 2, -2, -1 },
20979 { 2, 0, -2, -6, -2 },
20980
20981 /* 281-290 */
20982 { 1, 0, -2, 1, -2 },
20983 { 1, 0, -2, 2, 1 },
20984 { 1, -1, 0, 2, -1 },
20985 { 1, 0, -2, 1, 0 },
20986 { 2, -1, 0, -2, 1 },
20987 { 1, -1, 0, 2, 1 },
20988 { 2, 0, -2, -2, 0 },
20989 { 1, 0, 2, -3, 2 },
20990 { 0, 0, 0, 4, -1 },
20991 { 2, -1, 0, 0, 1 },
20992
20993 /* 291-300 */
20994 { 2, 0, 4, -2, 2 },
20995 { 0, 0, 2, 3, 2 },
20996 { 0, 1, 4, -2, 2 },
20997 { 0, 1, -2, 2, 1 },
20998 { 1, 1, 0, 2, 1 },
20999 { 1, 0, 0, 4, 1 },
21000 { 0, 0, 4, 0, 1 },
21001 { 2, 0, 0, -3, 0 },
21002 { 1, 0, 0, -1, -2 },
21003 { 1, -2, -2, -2, -2 },
21004
21005 /* 301-310 */
21006 { 3, 0, 0, 2, 0 },
21007 { 2, 0, 2, -4, 2 },
21008 { 1, 1, -2, -4, -1 },
21009 { 1, 0, -2, -6, -2 },
21010 { 2, -1, 0, 0, -1 },
21011 { 2, -1, 0, 2, 0 },
21012 { 0, 1, 2, -2, -1 },
21013 { 1, 1, 0, 1, 0 },
21014 { 1, 2, 0, -2, -1 },
21015 { 1, 0, 0, 1, -1 },
21016
21017 /* 311-320 */
21018 { 0, 0, 1, 0, 2 },
21019 { 3, 1, 2, -2, 2 },
21020 { 1, 0, -4, -2, -2 },
21021 { 1, 0, 2, 4, 1 },
21022 { 1, -2, 2, 2, 2 },
21023 { 1, -1, -2, -4, -2 },
21024 { 0, 0, 2, -4, 2 },
21025 { 0, 0, 2, -3, 1 },
21026 { 2, 1, -2, 0, 0 },
21027 { 3, 0, -2, -2, -1 },
21028
21029 /* 321-330 */
21030 { 2, 0, 2, 4, 2 },
21031 { 0, 0, 0, 0, 3 },
21032 { 2, -1, -2, -2, -2 },
21033 { 2, 0, 0, -1, 0 },
21034 { 3, 0, 2, -4, 2 },
21035 { 2, 1, 2, 2, 2 },
21036 { 0, 0, 3, 0, 3 },
21037 { 1, 1, 2, 2, 1 },
21038 { 2, 1, 0, 0, -1 },
21039 { 1, 2, 0, -2, 1 },
21040
21041 /* 331-340 */
21042 { 3, 0, 2, 2, 1 },
21043 { 1, -1, -2, 2, -2 },
21044 { 1, 1, 0, -1, 0 },
21045 { 1, 2, 0, 0, 0 },
21046 { 1, 0, 4, 0, 2 },
21047 { 1, -1, 2, 4, 2 },
21048 { 2, 1, 0, 0, 1 },
21049 { 1, 0, 0, 2, 2 },
21050 { 1, -1, -2, 2, 0 },
21051 { 0, 2, -2, -2, -1 },
21052
21053 /* 341-350 */
21054 { 2, 0, -2, 0, 2 },
21055 { 5, 0, 2, 0, 2 },
21056 { 3, 0, -2, -6, -2 },
21057 { 1, -1, 2, -1, 2 },
21058 { 3, 0, 0, -4, -1 },
21059 { 1, 0, 0, 1, 1 },
21060 { 1, 0, -4, 2, -1 },
21061 { 0, 1, 2, -4, 1 },
21062 { 1, 2, 2, 0, 2 },
21063 { 0, 1, 0, -2, -2 },
21064
21065 /* 351-360 */
21066 { 0, 0, 2, -1, 0 },
21067 { 1, 0, 1, 0, 1 },
21068 { 0, 2, 0, -2, 1 },
21069 { 3, 0, 2, 0, 0 },
21070 { 1, 1, -2, 1, 0 },
21071 { 2, 1, -2, -4, -1 },
21072 { 3, -1, 0, 0, 0 },
21073 { 2, -1, -2, 0, 0 },
21074 { 4, 0, 2, -2, 1 },
21075 { 2, 0, -2, 2, 0 },
21076
21077 /* 361-370 */
21078 { 1, 1, 2, -2, 0 },
21079 { 1, 0, -2, 4, -1 },
21080 { 1, 0, -2, -2, 1 },
21081 { 2, 0, 2, -4, 0 },
21082 { 1, 1, 0, -2, -2 },
21083 { 1, 1, -2, -2, 0 },
21084 { 1, 0, 1, -2, 1 },
21085 { 2, -1, -2, -4, -2 },
21086 { 3, 0, -2, 0, -2 },
21087 { 0, 1, -2, -2, 0 },
21088
21089 /* 371-380 */
21090 { 3, 0, 0, -2, -1 },
21091 { 1, 0, -2, -3, -1 },
21092 { 0, 1, 0, -4, -1 },
21093 { 1, -2, 2, -2, 1 },
21094 { 0, 1, -2, 1, -1 },
21095 { 1, -1, 0, 0, 2 },
21096 { 2, 0, 0, 1, 0 },
21097 { 1, -2, 0, 2, 0 },
21098 { 1, 2, -2, -2, -1 },
21099 { 0, 0, 4, -4, 1 },
21100
21101 /* 381-390 */
21102 { 0, 1, 2, 4, 2 },
21103 { 0, 1, -4, 2, -2 },
21104 { 3, 0, -2, 0, 0 },
21105 { 2, -1, 2, 2, 1 },
21106 { 0, 1, -2, -4, -1 },
21107 { 4, 0, 2, 2, 2 },
21108 { 2, 0, -2, -3, -2 },
21109 { 2, 0, 0, -6, 0 },
21110 { 1, 0, 2, 0, 3 },
21111 { 3, 1, 0, 0, 0 },
21112
21113 /* 391-400 */
21114 { 3, 0, 0, -4, 1 },
21115 { 1, -1, 2, 0, 0 },
21116 { 1, -1, 0, -4, 0 },
21117 { 2, 0, -2, 2, -2 },
21118 { 1, 1, 0, -2, 2 },
21119 { 4, 0, 0, -2, 0 },
21120 { 2, 2, 0, -2, 0 },
21121 { 0, 1, 2, 0, 0 },
21122 { 1, 1, 0, -4, 1 },
21123 { 1, 0, 0, -4, -2 },
21124
21125 /* 401-410 */
21126 { 0, 0, 0, 1, 2 },
21127 { 3, 0, 0, 2, 1 },
21128 { 1, 1, 0, -4, -1 },
21129 { 0, 0, 2, 2, -1 },
21130 { 1, 1, 2, 0, 0 },
21131 { 1, -1, 2, -4, 1 },
21132 { 1, 1, 0, 0, 2 },
21133 { 0, 0, 2, 6, 2 },
21134 { 4, 0, -2, -2, -1 },
21135 { 2, 1, 0, -4, -1 },
21136
21137 /* 411-420 */
21138 { 0, 0, 0, 3, 1 },
21139 { 1, -1, -2, 0, 0 },
21140 { 0, 0, 2, 1, 0 },
21141 { 1, 0, 0, 2, -2 },
21142 { 3, -1, 2, 2, 2 },
21143 { 3, -1, 2, -2, 2 },
21144 { 1, 0, 0, -1, 2 },
21145 { 1, -2, 2, -2, 2 },
21146 { 0, 1, 0, 2, 2 },
21147 { 0, 1, -2, -1, -2 },
21148
21149 /* 421-430 */
21150 { 1, 1, -2, 0, 0 },
21151 { 0, 2, 2, -2, 0 },
21152 { 3, -1, -2, -1, -2 },
21153 { 1, 0, 0, -6, 0 },
21154 { 1, 0, -2, -4, 0 },
21155 { 2, 1, 0, -4, 1 },
21156 { 2, 0, 2, 0, -1 },
21157 { 2, 0, -4, 0, -1 },
21158 { 0, 0, 3, 0, 2 },
21159 { 2, 1, -2, -2, -1 },
21160
21161 /* 431-440 */
21162 { 1, -2, 0, 0, 1 },
21163 { 2, -1, 0, -4, 0 },
21164 { 0, 0, 0, 3, 0 },
21165 { 5, 0, 2, -2, 2 },
21166 { 1, 2, -2, -4, -2 },
21167 { 1, 0, 4, -4, 2 },
21168 { 0, 0, 4, -1, 2 },
21169 { 3, 1, 0, -4, 0 },
21170 { 3, 0, 0, -6, 0 },
21171 { 2, 0, 0, 2, 2 },
21172
21173 /* 441-450 */
21174 { 2, -2, 2, 0, 2 },
21175 { 1, 0, 0, -3, 1 },
21176 { 1, -2, -2, 0, -2 },
21177 { 1, -1, -2, -3, -2 },
21178 { 0, 0, 2, -2, -2 },
21179 { 2, 0, -2, -4, 0 },
21180 { 1, 0, -4, 0, 0 },
21181 { 0, 1, 0, -1, 0 },
21182 { 4, 0, 0, 0, -1 },
21183 { 3, 0, 2, -1, 2 },
21184
21185 /* 451-460 */
21186 { 3, -1, 2, 0, 1 },
21187 { 2, 0, 2, -1, 1 },
21188 { 1, 2, 2, -2, 1 },
21189 { 1, 1, 0, 2, -1 },
21190 { 0, 2, 2, 0, 1 },
21191 { 3, 1, 2, 0, 1 },
21192 { 1, 1, 2, 1, 1 },
21193 { 1, 1, 0, -1, 1 },
21194 { 1, -2, 0, -2, -1 },
21195 { 4, 0, 0, -4, 0 },
21196
21197 /* 461-470 */
21198 { 2, 1, 0, 2, 0 },
21199 { 1, -1, 0, 4, 0 },
21200 { 0, 1, 0, -2, 2 },
21201 { 0, 0, 2, 0, -2 },
21202 { 1, 0, -1, 0, 1 },
21203 { 3, 0, 2, -2, 0 },
21204 { 2, 0, 2, 2, 0 },
21205 { 1, 2, 0, -4, 0 },
21206 { 1, -1, 0, -3, 0 },
21207 { 0, 1, 0, 4, 0 },
21208
21209 /* 471 - 480 */
21210 { 0, 1, -2, 0, 0 },
21211 { 2, 2, 2, -2, 2 },
21212 { 0, 0, 0, 1, -2 },
21213 { 0, 2, -2, 0, -1 },
21214 { 4, 0, 2, -4, 2 },
21215 { 2, 0, -4, 2, -2 },
21216 { 2, -1, -2, 0, -2 },
21217 { 1, 1, 4, -2, 2 },
21218 { 1, 1, 2, -4, 2 },
21219 { 1, 0, 2, 3, 2 },
21220
21221 /* 481-490 */
21222 { 1, 0, 0, 4, -1 },
21223 { 0, 0, 0, 4, 2 },
21224 { 2, 0, 0, 4, 0 },
21225 { 1, 1, -2, 2, 0 },
21226 { 2, 1, 2, 1, 2 },
21227 { 2, 1, 2, -4, 1 },
21228 { 2, 0, 2, 1, 1 },
21229 { 2, 0, -4, -2, -1 },
21230 { 2, 0, -2, -6, -1 },
21231 { 2, -1, 2, -1, 2 },
21232
21233 /* 491-500 */
21234 { 1, -2, 2, 0, 1 },
21235 { 1, -2, 0, -2, 1 },
21236 { 1, -1, 0, -4, -1 },
21237 { 0, 2, 2, 2, 2 },
21238 { 0, 2, -2, -4, -2 },
21239 { 0, 1, 2, 3, 2 },
21240 { 0, 1, 0, -4, 1 },
21241 { 3, 0, 0, -2, 1 },
21242 { 2, 1, -2, 0, 1 },
21243 { 2, 0, 4, -2, 1 },
21244
21245 /* 501-510 */
21246 { 2, 0, 0, -3, -1 },
21247 { 2, -2, 0, -2, 1 },
21248 { 2, -1, 2, -2, 1 },
21249 { 1, 0, 0, -6, -1 },
21250 { 1, -2, 0, 0, -1 },
21251 { 1, -2, -2, -2, -1 },
21252 { 0, 1, 4, -2, 1 },
21253 { 0, 0, 2, 3, 1 },
21254 { 2, -1, 0, -1, 0 },
21255 { 1, 3, 0, -2, 0 },
21256
21257 /* 511-520 */
21258 { 0, 3, 0, -2, 0 },
21259 { 2, -2, 2, -2, 2 },
21260 { 0, 0, 4, -2, 0 },
21261 { 4, -1, 2, 0, 2 },
21262 { 2, 2, -2, -4, -2 },
21263 { 4, 1, 2, 0, 2 },
21264 { 4, -1, -2, -2, -2 },
21265 { 2, 1, 0, -2, -2 },
21266 { 2, 1, -2, -6, -2 },
21267 { 2, 0, 0, -1, 1 },
21268
21269 /* 521-530 */
21270 { 2, -1, -2, 2, -1 },
21271 { 1, 1, -2, 2, -2 },
21272 { 1, 1, -2, -3, -2 },
21273 { 1, 0, 3, 0, 3 },
21274 { 1, 0, -2, 1, 1 },
21275 { 1, 0, -2, 0, 2 },
21276 { 1, -1, 2, 1, 2 },
21277 { 1, -1, 0, 0, -2 },
21278 { 1, -1, -4, 2, -2 },
21279 { 0, 3, -2, -2, -2 },
21280
21281 /* 531-540 */
21282 { 0, 1, 0, 4, 1 },
21283 { 0, 0, 4, 2, 2 },
21284 { 3, 0, -2, -2, 0 },
21285 { 2, -2, 0, 0, 0 },
21286 { 1, 1, 2, -4, 0 },
21287 { 1, 1, 0, -3, 0 },
21288 { 1, 0, 2, -3, 0 },
21289 { 1, -1, 2, -2, 0 },
21290 { 0, 2, 0, 2, 0 },
21291 { 0, 0, 2, 4, 0 },
21292
21293 /* 541-550 */
21294 { 1, 0, 1, 0, 0 },
21295 { 3, 1, 2, -2, 1 },
21296 { 3, 0, 4, -2, 2 },
21297 { 3, 0, 2, 1, 2 },
21298 { 3, 0, 0, 2, -1 },
21299 { 3, 0, 0, 0, 2 },
21300 { 3, 0, -2, 2, -1 },
21301 { 2, 0, 4, -4, 2 },
21302 { 2, 0, 2, -3, 2 },
21303 { 2, 0, 0, 4, 1 },
21304
21305 /* 551-560 */
21306 { 2, 0, 0, -3, 1 },
21307 { 2, 0, -4, 2, -1 },
21308 { 2, 0, -2, -2, 1 },
21309 { 2, -2, 2, 2, 2 },
21310 { 2, -2, 0, -2, -2 },
21311 { 2, -1, 0, 2, 1 },
21312 { 2, -1, 0, 2, -1 },
21313 { 1, 1, 2, 4, 2 },
21314 { 1, 1, 0, 1, 1 },
21315 { 1, 1, 0, 1, -1 },
21316
21317 /* 561-570 */
21318 { 1, 1, -2, -6, -2 },
21319 { 1, 0, 0, -3, -1 },
21320 { 1, 0, -4, -2, -1 },
21321 { 1, 0, -2, -6, -1 },
21322 { 1, -2, 2, 2, 1 },
21323 { 1, -2, -2, 2, -1 },
21324 { 1, -1, -2, -4, -1 },
21325 { 0, 2, 0, 0, 2 },
21326 { 0, 1, 2, -4, 2 },
21327 { 0, 1, -2, 4, -1 },
21328
21329 /* 571-580 */
21330 { 5, 0, 0, 0, 0 },
21331 { 3, 0, 0, -3, 0 },
21332 { 2, 2, 0, -4, 0 },
21333 { 1, -1, 2, 2, 0 },
21334 { 0, 1, 0, 3, 0 },
21335 { 4, 0, -2, 0, -1 },
21336 { 3, 0, -2, -6, -1 },
21337 { 3, 0, -2, -1, -1 },
21338 { 2, 1, 2, 2, 1 },
21339 { 2, 1, 0, 2, 1 },
21340
21341 /* 581-590 */
21342 { 2, 0, 2, 4, 1 },
21343 { 2, 0, 2, -6, 1 },
21344 { 2, 0, 2, -2, -1 },
21345 { 2, 0, 0, -6, -1 },
21346 { 2, -1, -2, -2, -1 },
21347 { 1, 2, 2, 0, 1 },
21348 { 1, 2, 0, 0, 1 },
21349 { 1, 0, 4, 0, 1 },
21350 { 1, 0, 2, -6, 1 },
21351 { 1, 0, 2, -4, -1 },
21352
21353 /* 591-600 */
21354 { 1, 0, -1, -2, -1 },
21355 { 1, -1, 2, 4, 1 },
21356 { 1, -1, 2, -3, 1 },
21357 { 1, -1, 0, 4, 1 },
21358 { 1, -1, -2, 1, -1 },
21359 { 0, 1, 2, -2, 3 },
21360 { 3, 0, 0, -2, 0 },
21361 { 1, 0, 1, -2, 0 },
21362 { 0, 2, 0, -4, 0 },
21363 { 0, 0, 2, -4, 0 },
21364
21365 /* 601-610 */
21366 { 0, 0, 1, -1, 0 },
21367 { 0, 0, 0, 6, 0 },
21368 { 0, 2, 0, 0, -2 },
21369 { 0, 1, -2, 2, -3 },
21370 { 4, 0, 0, 2, 0 },
21371 { 3, 0, 0, -1, 0 },
21372 { 3, -1, 0, 2, 0 },
21373 { 2, 1, 0, 1, 0 },
21374 { 2, 1, 0, -6, 0 },
21375 { 2, -1, 2, 0, 0 },
21376
21377 /* 611-620 */
21378 { 1, 0, 2, -1, 0 },
21379 { 1, -1, 0, 1, 0 },
21380 { 1, -1, -2, -2, 0 },
21381 { 0, 1, 2, 2, 0 },
21382 { 0, 0, 2, -3, 0 },
21383 { 2, 2, 0, -2, -1 },
21384 { 2, -1, -2, 0, 1 },
21385 { 1, 2, 2, -4, 1 },
21386 { 0, 1, 4, -4, 2 },
21387 { 0, 0, 0, 3, 2 },
21388
21389 /* 621-630 */
21390 { 5, 0, 2, 0, 1 },
21391 { 4, 1, 2, -2, 2 },
21392 { 4, 0, -2, -2, 0 },
21393 { 3, 1, 2, 2, 2 },
21394 { 3, 1, 0, -2, 0 },
21395 { 3, 1, -2, -6, -2 },
21396 { 3, 0, 0, 0, -2 },
21397 { 3, 0, -2, -4, -2 },
21398 { 3, -1, 0, -3, 0 },
21399 { 3, -1, 0, -2, 0 },
21400
21401 /* 631-640 */
21402 { 2, 1, 2, 0, 0 },
21403 { 2, 1, 2, -4, 2 },
21404 { 2, 1, 2, -2, 0 },
21405 { 2, 1, 0, -3, 0 },
21406 { 2, 1, -2, 0, -2 },
21407 { 2, 0, 0, -4, 2 },
21408 { 2, 0, 0, -4, -2 },
21409 { 2, 0, -2, -5, -2 },
21410 { 2, -1, 2, 4, 2 },
21411 { 2, -1, 0, -2, 2 },
21412
21413 /* 641-650 */
21414 { 1, 3, -2, -2, -2 },
21415 { 1, 1, 0, 0, -2 },
21416 { 1, 1, 0, -6, 0 },
21417 { 1, 1, -2, 1, -2 },
21418 { 1, 1, -2, -1, -2 },
21419 { 1, 0, 2, 1, 0 },
21420 { 1, 0, 0, 3, 0 },
21421 { 1, 0, 0, -4, 2 },
21422 { 1, 0, -2, 4, -2 },
21423 { 1, -2, 0, -1, 0 },
21424
21425 /* 651-NFLS */
21426 { 0, 1, -4, 2, -1 },
21427 { 1, 0, -2, 0, -3 },
21428 { 0, 0, 4, -4, 4 }
21429 };
21430 }
21431
21432
21433 /* Fundamental-argument multipliers: planetary terms */
21434 private static final int mfapl[][] = {
21435
21436 /* 1-10 */
21437 { 0, 0, 1, -1, 1, 0, 0, -1, 0, -2, 5, 0, 0, 0 },
21438 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, -1 },
21439 { 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, -2 },
21440 { 0, 0, 1, -1, 1, 0, -8, 12, 0, 0, 0, 0, 0, 0 },
21441 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2 },
21442 { 0, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0 },
21443 { 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0 },
21444 { 0, 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, 0 },
21445 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0 },
21446 { 0, 0, 0, 0, 1, 0, 0, -1, 2, 0, 0, 0, 0, 0 },
21447
21448 /* 11-20 */
21449 { 0, 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, -1 },
21450 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 2, -5, 0, 0, 0 },
21451 { 0, 0, 2, -2, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0 },
21452 { 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, -2 },
21453 { 0, 0, 0, 0, 0, 0, 0, 3, 0, -1, 0, 0, 0, 2 },
21454 { 0, 0, 0, 0, 0, 0, 0, 2, -8, 3, 0, 0, 0, -2 },
21455 { 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, -2 },
21456 { 0, 0, 0, 0, 0, 0, 0, 6, -8, 3, 0, 0, 0, 2 },
21457 { 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0 },
21458 { 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 0 },
21459
21460 /* 21-30 */
21461 { 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0 },
21462 { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2 },
21463 { 0, 0, 0, 0, 1, 0, 0, -4, 8, -3, 0, 0, 0, 0 },
21464 { 0, 0, 0, 0, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0 },
21465 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0 },
21466 { 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2 },
21467 { 0, 0, 1, -1, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0 },
21468 { 2, 0, 0, -2, -1, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
21469 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1 },
21470 { 2, 0, 0, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
21471
21472 /* 31-40 */
21473 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0 },
21474 { 0, 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, 0 },
21475 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2 },
21476 { 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, -2 },
21477 { 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0 },
21478 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 1 },
21479 { 2, 0, 0, -2, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
21480 { 0, 0, 1, -1, 1, 0, 0, -1, 0, -1, 0, 0, 0, 0 },
21481 { 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0 },
21482 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0 },
21483
21484 /* 41-50 */
21485 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0 },
21486 { 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, -2 },
21487 { 0, 0, 1, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0 },
21488 { 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 2 },
21489 { 0, 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, -2 },
21490 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 },
21491 { 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 2 },
21492 { 1, 0, 0, 0, 0, 0,-18, 16, 0, 0, 0, 0, 0, 0 },
21493 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0 },
21494 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2 },
21495
21496 /* 51-60 */
21497 { 0, 0, 1, -1, 1, 0, -5, 7, 0, 0, 0, 0, 0, 0 },
21498 { 1, 0, 0, 0, 0, 0,-10, 3, 0, 0, 0, 0, 0, 0 },
21499 { 0, 0, 2, -2, 0, 0, -5, 6, 0, 0, 0, 0, 0, 0 },
21500 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 2 },
21501 { 1, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
21502 { 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 2 },
21503 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1 },
21504 { 1, 0, -2, 0, -2, 0, 0, 4, -8, 3, 0, 0, 0, 0 },
21505 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 2, 0, 0, 0 },
21506 { 0, 0, 2, -2, 1, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
21507
21508 /* 61-70 */
21509 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2 },
21510 { 0, 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, -2 },
21511 { 0, 0, 1, -1, 1, 0, 0, 3, -8, 3, 0, 0, 0, 0 },
21512 { 0, 0, 0, 0, 0, 0, 8,-11, 0, 0, 0, 0, 0, -2 },
21513 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2 },
21514 { 0, 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, 2 },
21515 { 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1 },
21516 { 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, -1 },
21517 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, -2 },
21518 { 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0 },
21519
21520 /* 71-80 */
21521 { 0, 0, 0, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, -2 },
21522 { 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 2 },
21523 { 0, 0, 0, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0, -2 },
21524 { 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0, 0, 0, -2 },
21525 { 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, -2 },
21526 { 0, 0, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 2 },
21527 { 0, 0, 1, -1, 1, 0, 0, -5, 8, -3, 0, 0, 0, 0 },
21528 { 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2 },
21529 { 0, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 2 },
21530 { 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, 0 },
21531
21532 /* 81-90 */
21533 { 2, 0, 0, -2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
21534 { 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, -1 },
21535 { 2, 0, 0, -2, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
21536 { 0, 0, 0, 0, 1, 0, 8,-13, 0, 0, 0, 0, 0, 0 },
21537 { 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 5, 0, 0, 0 },
21538 { 1, 0, 0, -1, 0, 0, -3, 4, 0, 0, 0, 0, 0, 0 },
21539 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2 },
21540 { 1, 0, 0, 0, -1, 0,-18, 16, 0, 0, 0, 0, 0, 0 },
21541 { 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, -5, 0, 0, 0 },
21542 { 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0 },
21543
21544 /* 91-100 */
21545 { 1, 0, 0, -2, 0, 0, 19,-21, 3, 0, 0, 0, 0, 0 },
21546 { 0, 0, 0, 0, 1, 0, -8, 13, 0, 0, 0, 0, 0, 0 },
21547 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0 },
21548 { 0, 0, 0, 0, 0, 0, 7, -9, 0, 0, 0, 0, 0, -2 },
21549 { 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2 },
21550 { 1, 0, 0, 0, 1, 0,-18, 16, 0, 0, 0, 0, 0, 0 },
21551 { 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, -1 },
21552 { 0, 0, 0, 0, 0, 0, 0, 6,-16, 4, 5, 0, 0, -2 },
21553 { 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, 0, -2 },
21554 { 0, 0, 0, 0, 0, 0, 3, -7, 0, 0, 0, 0, 0, -2 },
21555
21556 /* 101-110 */
21557 { 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -1 },
21558 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 },
21559 { 2, 0, 0, -2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
21560 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1 },
21561 { 0, 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0 },
21562 { 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0 },
21563 { 2, 0, 0, -2, -1, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
21564 { 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0 },
21565 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0 },
21566 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2 },
21567
21568 /* 111-120 */
21569 { 0, 0, 0, 0, 1, 0, 0, 1, -2, 0, 0, 0, 0, 0 },
21570 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2 },
21571 { 0, 0, 2, -2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
21572 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, 0 },
21573 { 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, -1 },
21574 { 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 2 },
21575 { 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0 },
21576 { 0, 0, 1, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0 },
21577 { 2, 0, 0, -2, 0, 0, -6, 8, 0, 0, 0, 0, 0, 0 },
21578 { 0, 0, 1, -1, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0 },
21579
21580 /* 121-130 */
21581 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1 },
21582 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
21583 { 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, -1 },
21584 { 0, 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0 },
21585 { 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, -2 },
21586 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0 },
21587 { 0, 0, 0, 0, 0, 0, 8,-10, 0, 0, 0, 0, 0, -2 },
21588 { 0, 0, 1, -1, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0 },
21589 { 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, -2 },
21590 { 1, 0, 0, -1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0 },
21591
21592 /* 131-140 */
21593 { 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, -1 },
21594 { 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 0 },
21595 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1 },
21596 { 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, -1 },
21597 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 },
21598 { 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2 },
21599 { 0, 0, 0, 0, 0, 0, 0, 4, 0, -3, 0, 0, 0, 2 },
21600 { 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1 },
21601 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1 },
21602 { 0, 0, 0, 0, 1, 0, 2, -3, 0, 0, 0, 0, 0, 0 },
21603
21604 /* 141-150 */
21605 { 1, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
21606 { 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, -1 },
21607 { 0, 0, 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 2 },
21608 { 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 2 },
21609 { 0, 0, 0, 0, 0, 0, 9,-11, 0, 0, 0, 0, 0, -2 },
21610 { 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, -1 },
21611 { 0, 0, 0, 0, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0 },
21612 { 0, 0, 1, -1, 1, 0, -4, 5, 0, 0, 0, 0, 0, 0 },
21613 { 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, 0 },
21614 { 0, 0, 0, 0, 0, 0, 0, 4, 0, -1, 0, 0, 0, 2 },
21615
21616 /* 151-160 */
21617 { 1, 0, 0, -1, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0 },
21618 { 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
21619 { 0, 0, 1, -1, 1, 0, 0, -1, 0, -4, 10, 0, 0, 0 },
21620 { 0, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0 },
21621 { 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 },
21622 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, 0 },
21623 { 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 2 },
21624 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, -2 },
21625 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, -2 },
21626 { 0, 0, 2, -2, 1, 0, -4, 4, 0, 0, 0, 0, 0, 0 },
21627
21628 /* 161-170 */
21629 { 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, 2 },
21630 { 0, 0, 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 2 },
21631 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 2, 0 },
21632 { 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, -1 },
21633 { 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, -1 },
21634 { 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, 0 },
21635 { 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 1 },
21636 { 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0 },
21637 { 0, 0, 2, -2, 1, 0, 0, -9, 13, 0, 0, 0, 0, 0 },
21638 { 2, 0, 2, 0, 2, 0, 0, 2, 0, -3, 0, 0, 0, 0 },
21639
21640 /* 171-180 */
21641 { 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, -2 },
21642 { 0, 0, 1, -1, 2, 0, 0, -1, 0, 0, 2, 0, 0, 0 },
21643 { 1, 0, 0, -1, -1, 0, -3, 4, 0, 0, 0, 0, 0, 0 },
21644 { 0, 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, -2 },
21645 { 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 0 },
21646 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1 },
21647 { 1, 0, 2, 0, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
21648 { 1, 0, -2, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0 },
21649 { 0, 0, 0, 0, 1, 0, 0, -2, 4, 0, 0, 0, 0, 0 },
21650 { 0, 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0 },
21651
21652 /* 181-190 */
21653 { 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2 },
21654 { 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1 },
21655 { 0, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
21656 { 0, 0, 0, 0, 0, 0, 0, 1, -8, 3, 0, 0, 0, -2 },
21657 { 0, 0, 0, 0, 0, 0, 6,-10, 0, 0, 0, 0, 0, -2 },
21658 { 0, 0, 0, 0, 0, 0, 0, 7, -8, 3, 0, 0, 0, 2 },
21659 { 0, 0, 0, 0, 1, 0, -3, 5, 0, 0, 0, 0, 0, 0 },
21660 { 0, 0, 1, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0 },
21661 { 0, 0, 1, -1, 0, 0, -5, 7, 0, 0, 0, 0, 0, 0 },
21662 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 1 },
21663
21664 /* 191-200 */
21665 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0 },
21666 { 0, 0, 0, 0, 0, 0, 7,-10, 0, 0, 0, 0, 0, -2 },
21667 { 1, 0, 0, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
21668 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0 },
21669 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, -5, 0, 0, 0 },
21670 { 0, 0, 0, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, -1 },
21671 { 0, 0, 1, -1, 1, 0, 0, -9, 15, 0, 0, 0, 0, 0 },
21672 { 0, 0, 0, 0, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0 },
21673 { 0, 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0 },
21674 { 0, 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0 },
21675
21676 /* 201-210 */
21677 { 0, 0, 0, 0, 0, 0, 0, 1, -4, 0, 0, 0, 0, -2 },
21678 { 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 2 },
21679 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 2 },
21680 { 2, 0, 0, -2, 1, 0, -6, 8, 0, 0, 0, 0, 0, 0 },
21681 { 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, -1 },
21682 { 0, 0, 1, -1, 1, 0, 3, -6, 0, 0, 0, 0, 0, 0 },
21683 { 0, 0, 1, -1, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0 },
21684 { 0, 0, 1, -1, 1, 0, 8,-14, 0, 0, 0, 0, 0, 0 },
21685 { 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 },
21686 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
21687
21688 /* 211-220 */
21689 { 0, 0, 0, 0, 1, 0, 0, 8,-15, 0, 0, 0, 0, 0 },
21690 { 0, 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0 },
21691 { 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 0, 0 },
21692 { 2, 0, 0, -2, 1, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
21693 { 0, 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 2 },
21694 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2 },
21695 { 2, 0, -1, -1, 0, 0, 0, 3, -7, 0, 0, 0, 0, 0 },
21696 { 0, 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, -2 },
21697 { 0, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0 },
21698 { 0, 0, 1, -1, 1, 0, 0, -3, 4, 0, 0, 0, 0, 0 },
21699
21700 /* 221-230 */
21701 { 2, 0, 0, -2, 0, 0, 0, -6, 8, 0, 0, 0, 0, 0 },
21702 { 2, 0, 0, -2, 0, 0, 0, -5, 6, 0, 0, 0, 0, 0 },
21703 { 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0 },
21704 { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1 },
21705 { 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1 },
21706 { 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2 },
21707 { 0, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0 },
21708 { 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0 },
21709 { 0, 0, 0, 0, 0, 0, 3, -9, 4, 0, 0, 0, 0, -2 },
21710 { 0, 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, -2 },
21711
21712 /* 231-240 */
21713 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, -2 },
21714 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1 },
21715 { 0, 0, 0, 0, 0, 0, 7,-11, 0, 0, 0, 0, 0, -2 },
21716 { 0, 0, 0, 0, 0, 0, 3, -5, 4, 0, 0, 0, 0, 2 },
21717 { 0, 0, 1, -1, 0, 0, 0, -1, 0, -1, 1, 0, 0, 0 },
21718 { 2, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
21719 { 0, 0, 0, 0, 0, 0, 0, 8,-15, 0, 0, 0, 0, -2 },
21720 { 0, 0, 1, -1, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0 },
21721 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2 },
21722 { 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, -1 },
21723
21724 /* 241-250 */
21725 { 0, 0, 1, -1, 1, 0, 0, -1, 0, -1, 1, 0, 0, 0 },
21726 { 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 1 },
21727 { 0, 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, 0 },
21728 { 0, 0, 0, 0, 0, 0, 0, 3, -8, 3, 0, 0, 0, 0 },
21729 { 0, 0, 1, -1, 1, 0, 2, -4, 0, -3, 0, 0, 0, 0 },
21730 { 0, 0, 0, 0, 1, 0, 3, -5, 0, 2, 0, 0, 0, 0 },
21731 { 0, 0, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 2 },
21732 { 0, 0, 2, -2, 2, 0, -8, 11, 0, 0, 0, 0, 0, 0 },
21733 { 0, 0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 0 },
21734 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0 },
21735
21736 /* 251-260 */
21737 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2 },
21738 { 0, 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, -2 },
21739 { 0, 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 2 },
21740 { 0, 0, 0, 0, 0, 0, 7, -9, 0, 0, 0, 0, 0, -1 },
21741 { 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, 0, -1 },
21742 { 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0 },
21743 { 1, 0, -2, -2, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
21744 { 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2 },
21745 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 5, 0, 0, 2 },
21746 { 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 1 },
21747
21748 /* 261-270 */
21749 { 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2 },
21750 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -5, 0, 0, 2 },
21751 { 2, 0, 0, -2, -1, 0, 0, -2, 0, 0, 5, 0, 0, 0 },
21752 { 2, 0, 0, -2, -1, 0, -6, 8, 0, 0, 0, 0, 0, 0 },
21753 { 1, 0, 0, -2, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
21754 { 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0 },
21755 { 0, 0, 0, 0, 0, 0, 0, 3, 0, 2, -5, 0, 0, 2 },
21756 { 0, 0, 0, 0, 1, 0, 3, -7, 4, 0, 0, 0, 0, 0 },
21757 { 0, 0, 2, -2, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0 },
21758 { 0, 0, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
21759
21760 /* 271-280 */
21761 { 0, 0, 1, -1, 0, 0, 0, -1, 0, -2, 5, 0, 0, 0 },
21762 { 0, 0, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0 },
21763 { 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 1 },
21764 { 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, -2 },
21765 { 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 2 },
21766 { 0, 0, 0, 0, 0, 0, 0, 6,-15, 0, 0, 0, 0, -2 },
21767 { 0, 0, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 2 },
21768 { 1, 0, 0, -1, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0 },
21769 { 0, 0, 0, 0, 1, 0, -3, 7, -4, 0, 0, 0, 0, 0 },
21770 { 0, 0, 0, 0, 0, 0, 0, 5, 0, -2, 0, 0, 0, 2 },
21771
21772 /* 281-290 */
21773 { 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, 1 },
21774 { 0, 0, 2, -2, 2, 0, -5, 6, 0, 0, 0, 0, 0, 0 },
21775 { 0, 0, 2, -2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
21776 { 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2 },
21777 { 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0 },
21778 { 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 2 },
21779 { 0, 0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, -2 },
21780 { 0, 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0 },
21781 { 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, 0 },
21782 { 0, 0, 0, 0, 0, 0, 0, 6,-11, 0, 0, 0, 0, -2 },
21783
21784 /* 291-300 */
21785 { 0, 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, -2 },
21786 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 3, 0, 0, 0, 0 },
21787 { 0, 0, 1, -1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0 },
21788 { 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 1 },
21789 { 0, 0, 0, 0, 0, 0, 9,-12, 0, 0, 0, 0, 0, -2 },
21790 { 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 1 },
21791 { 0, 0, 1, -1, 0, 0, -8, 12, 0, 0, 0, 0, 0, 0 },
21792 { 0, 0, 1, -1, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0 },
21793 { 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 0, -1 },
21794 { 0, 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, -1 },
21795
21796 /* 301-310 */
21797 { 0, 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 2 },
21798 { 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, -2 },
21799 { 0, 0, 1, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
21800 { 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, -1 },
21801 { 0, 0, 1, -1, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0 },
21802 { 0, 0, 0, 0, 0, 0, 0, 1, -5, 0, 0, 0, 0, -2 },
21803 { 2, 0, 0, -2, 0, 0, 0, -2, 0, 3, -1, 0, 0, 0 },
21804 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0 },
21805 { 0, 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, 0 },
21806 { 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 2 },
21807
21808 /* 311-320 */
21809 { 0, 0, 0, 0, 0, 0, 9, -9, 0, 0, 0, 0, 0, -1 },
21810 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 3, 0, 0, 0 },
21811 { 0, 0, 0, 0, 1, 0, 0, 2, -4, 0, 0, 0, 0, 0 },
21812 { 0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 2 },
21813 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1 },
21814 { 0, 0, 1, -1, 2, 0, 0, -1, 0, 2, 0, 0, 0, 0 },
21815 { 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, 0, -2 },
21816 { 0, 0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 2 },
21817 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2 },
21818 { 0, 0, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0 },
21819
21820 /* 321-330 */
21821 { 0, 0, 2, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0 },
21822 { 0, 0, 0, 0, 0, 0, 0, 5, 0, -3, 0, 0, 0, 2 },
21823 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0 },
21824 { 2, 0, -1, -1, -1, 0, 0, -1, 0, 3, 0, 0, 0, 0 },
21825 { 0, 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 0, 2 },
21826 { 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 2 },
21827 { 0, 0, 0, 0, 0, 0, 5,-10, 0, 0, 0, 0, 0, -2 },
21828 { 0, 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, 1 },
21829 { 0, 0, 2, -2, 1, -1, 0, 2, 0, 0, 0, 0, 0, 0 },
21830 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 2, 0, 0 },
21831
21832 /* 331-340 */
21833 { 0, 0, 0, 0, 1, 0, 3, -5, 0, 0, 0, 0, 0, 0 },
21834 { 1, 0, 0, -2, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
21835 { 0, 0, 2, -2, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
21836 { 0, 0, 0, 0, 0, 0, 9, -9, 0, 0, 0, 0, 0, 0 },
21837 { 0, 0, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0 },
21838 { 0, 0, 2, -2, 1, 0, 0, -8, 11, 0, 0, 0, 0, 0 },
21839 { 0, 0, 2, -2, 1, 0, 0, -2, 0, 0, 2, 0, 0, 0 },
21840 { 0, 0, 1, -1, 1, 0, 0, -1, 0, -1, 2, 0, 0, 0 },
21841 { 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 2 },
21842 { 0, 0, 0, 0, 0, 0, 2, -6, 0, 0, 0, 0, 0, -2 },
21843
21844 /* 341-350 */
21845 { 0, 0, 0, 0, 0, 0, 0, 8,-15, 0, 0, 0, 0, -1 },
21846 { 0, 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, 0, 0, 2 },
21847 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2 },
21848 { 0, 0, 0, 0, 0, 0, 0, 7,-13, 0, 0, 0, 0, -2 },
21849 { 0, 0, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 0 },
21850 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 2 },
21851 { 0, 0, 2, -2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
21852 { 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, -1 },
21853 { 0, 0, 0, 0, 0, 0, 8,-10, 0, 0, 0, 0, 0, -1 },
21854 { 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 1 },
21855
21856 /* 351-360 */
21857 { 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, -1 },
21858 { 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, -1 },
21859 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 2 },
21860 { 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2 },
21861 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0 },
21862 { 2, 0, 0, -2, -1, 0, 0, -5, 6, 0, 0, 0, 0, 0 },
21863 { 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0, 0, -2 },
21864 { 2, 0, -1, -1, -1, 0, 0, 3, -7, 0, 0, 0, 0, 0 },
21865 { 0, 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0 },
21866 { 0, 0, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0 },
21867
21868 /* 361-370 */
21869 { 2, 0, 0, -2, 0, 0, 0, -2, 0, 4, -3, 0, 0, 0 },
21870 { 0, 0, 0, 0, 0, 0, 0, 6,-11, 0, 0, 0, 0, 0 },
21871 { 2, 0, 0, -2, 1, 0, 0, -6, 8, 0, 0, 0, 0, 0 },
21872 { 0, 0, 0, 0, 0, 0, 0, 4, -8, 1, 5, 0, 0, -2 },
21873 { 0, 0, 0, 0, 0, 0, 0, 6, -5, 0, 0, 0, 0, 2 },
21874 { 1, 0, -2, -2, -2, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
21875 { 0, 0, 1, -1, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0 },
21876 { 0, 0, 0, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0 },
21877 { 0, 0, 0, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0 },
21878 { 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1 },
21879
21880 /* 371-380 */
21881 { 0, 0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 2 },
21882 { 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 2 },
21883 { 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 2 },
21884 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1 },
21885 { 0, 0, 0, 0, 0, 0, 0, 1, -6, 0, 0, 0, 0, -2 },
21886 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 2 },
21887 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2 },
21888 { 0, 0, 0, 0, 0, 0, 3, -5, 0, 2, 0, 0, 0, 0 },
21889 { 0, 0, 0, 0, 0, 0, 0, 7,-13, 0, 0, 0, 0, 0 },
21890 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2 },
21891
21892 /* 381-390 */
21893 { 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0 },
21894 { 0, 0, 0, 0, 1, 0, 0, -8, 15, 0, 0, 0, 0, 0 },
21895 { 2, 0, 0, -2, -2, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
21896 { 2, 0, -1, -1, -1, 0, 0, -1, 0, 2, 0, 0, 0, 0 },
21897 { 1, 0, 2, -2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
21898 { 1, 0, -1, 1, -1, 0,-18, 17, 0, 0, 0, 0, 0, 0 },
21899 { 0, 0, 2, 0, 2, 0, 0, 1, 0, -1, 0, 0, 0, 0 },
21900 { 0, 0, 2, 0, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
21901 { 0, 0, 2, -2, -1, 0, -5, 6, 0, 0, 0, 0, 0, 0 },
21902 { 0, 0, 1, -1, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
21903
21904 /* 391-400 */
21905 { 0, 0, 0, 0, 1, 0, 2, -2, 0, 0, 0, 0, 0, 0 },
21906 { 0, 0, 0, 0, 0, 0, 8,-16, 0, 0, 0, 0, 0, -2 },
21907 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 2 },
21908 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2 },
21909 { 0, 0, 0, 0, 2, 0, 0, -1, 2, 0, 0, 0, 0, 0 },
21910 { 2, 0, -1, -1, -2, 0, 0, -1, 0, 2, 0, 0, 0, 0 },
21911 { 0, 0, 0, 0, 0, 0, 6,-10, 0, 0, 0, 0, 0, -1 },
21912 { 0, 0, 1, -1, 1, 0, 0, -1, 0, -2, 4, 0, 0, 0 },
21913 { 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2 },
21914 { 2, 0, 0, -2, -1, 0, 0, -2, 0, 4, -5, 0, 0, 0 },
21915
21916 /* 401-410 */
21917 { 2, 0, 0, -2, -1, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
21918 { 2, 0, -1, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0 },
21919 { 1, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0 },
21920 { 1, 0, 0, -1, -1, 0, 0, -2, 2, 0, 0, 0, 0, 0 },
21921 { 1, 0, -1, -1, -1, 0, 20,-20, 0, 0, 0, 0, 0, 0 },
21922 { 0, 0, 2, -2, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
21923 { 0, 0, 1, -1, 1, 0, 1, -2, 0, 0, 0, 0, 0, 0 },
21924 { 0, 0, 1, -1, 1, 0, -2, 1, 0, 0, 0, 0, 0, 0 },
21925 { 0, 0, 0, 0, 1, 0, 5, -8, 0, 0, 0, 0, 0, 0 },
21926 { 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0 },
21927
21928 /* 411-420 */
21929 { 0, 0, 0, 0, 0, 0, 9,-11, 0, 0, 0, 0, 0, -1 },
21930 { 0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 1 },
21931 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, -1 },
21932 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1 },
21933 { 0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 0, 0 },
21934 { 0, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0 },
21935 { 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -2 },
21936 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, -2, 0, 0, 0 },
21937 { 0, 0, 1, -1, 2, 0, 0, -1, 0, -2, 5, 0, 0, 0 },
21938 { 0, 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0 },
21939
21940 /* 421-430 */
21941 { 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, 0 },
21942 { 0, 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, -2 },
21943 { 0, 0, 0, 0, 0, 0, 0, 2, -6, 0, 0, 0, 0, -2 },
21944 { 1, 0, 0, -2, 0, 0, 20,-21, 0, 0, 0, 0, 0, 0 },
21945 { 0, 0, 0, 0, 0, 0, 8,-12, 0, 0, 0, 0, 0, 0 },
21946 { 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 0 },
21947 { 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0 },
21948 { 0, 0, 1, -1, 2, 0, 0, -1, 0, -1, 0, 0, 0, 0 },
21949 { 0, 0, 0, 0, 0, 0, 8,-12, 0, 0, 0, 0, 0, -2 },
21950 { 0, 0, 0, 0, 0, 0, 0, 9,-17, 0, 0, 0, 0, 0 },
21951
21952 /* 431-440 */
21953 { 0, 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 2 },
21954 { 0, 0, 0, 0, 0, 0, 0, 4, -8, 1, 5, 0, 0, 2 },
21955 { 0, 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, -2 },
21956 { 0, 0, 0, 0, 0, 0, 0, 2, -7, 0, 0, 0, 0, -2 },
21957 { 1, 0, 0, -1, 1, 0, 0, -3, 4, 0, 0, 0, 0, 0 },
21958 { 1, 0, -2, 0, -2, 0,-10, 3, 0, 0, 0, 0, 0, 0 },
21959 { 0, 0, 0, 0, 1, 0, 0, -9, 17, 0, 0, 0, 0, 0 },
21960 { 0, 0, 0, 0, 0, 0, 1, -4, 0, 0, 0, 0, 0, -2 },
21961 { 1, 0, -2, -2, -2, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
21962 { 1, 0, -1, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
21963
21964 /* 441-450 */
21965 { 0, 0, 2, -2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
21966 { 0, 0, 1, -1, 2, 0, 0, -1, 0, 0, 1, 0, 0, 0 },
21967 { 0, 0, 1, -1, 2, 0, -5, 7, 0, 0, 0, 0, 0, 0 },
21968 { 0, 0, 0, 0, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0 },
21969 { 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, -1 },
21970 { 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, -2 },
21971 { 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0 },
21972 { 0, 0, 0, 0, 0, 0, 0, 5,-10, 0, 0, 0, 0, -2 },
21973 { 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 2 },
21974 { 0, 0, 0, 0, 0, 0, 0, 2, 0, -5, 0, 0, 0, -2 },
21975
21976 /* 451-460 */
21977 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -5, 0, 0, 0, -2 },
21978 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 5, 0, 0, 2 },
21979 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, -2 },
21980 { 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 1 },
21981 { 1, 0, 0, -2, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0 },
21982 { 0, 0, 0, 0, 0, 0, 3, -7, 4, 0, 0, 0, 0, 0 },
21983 { 2, 0, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
21984 { 0, 0, 1, -1, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0 },
21985 { 0, 0, 0, 0, 1, 0, 0, 1, 0, -2, 0, 0, 0, 0 },
21986 { 0, 0, 0, 0, 0, 0, 0, 6,-10, 0, 0, 0, 0, -2 },
21987
21988 /* 461-470 */
21989 { 1, 0, 0, -1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
21990 { 0, 0, 2, -2, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0 },
21991 { 0, 0, 2, -2, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0 },
21992 { 0, 0, 2, -2, 1, 0, 0, -4, 8, -3, 0, 0, 0, 0 },
21993 { 0, 0, 2, -2, 1, 0, 0, -3, 0, 3, 0, 0, 0, 0 },
21994 { 0, 0, 2, -2, 1, 0, -5, 5, 0, 0, 0, 0, 0, 0 },
21995 { 0, 0, 1, -1, 1, 0, 1, -3, 0, 0, 0, 0, 0, 0 },
21996 { 0, 0, 1, -1, 1, 0, 0, -4, 6, 0, 0, 0, 0, 0 },
21997 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, -1, 0, 0 },
21998 { 0, 0, 1, -1, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0 },
21999
22000 /* 471-480 */
22001 { 0, 0, 0, 0, 1, 0, 3, -4, 0, 0, 0, 0, 0, 0 },
22002 { 0, 0, 0, 0, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0 },
22003 { 0, 0, 0, 0, 0, 0, 7,-10, 0, 0, 0, 0, 0, -1 },
22004 { 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 1 },
22005 { 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, -2 },
22006 { 0, 0, 0, 0, 0, 0, 3, -8, 0, 0, 0, 0, 0, -2 },
22007 { 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0, 0, 0, -1 },
22008 { 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -1 },
22009 { 0, 0, 0, 0, 0, 0, 0, 7, -9, 0, 0, 0, 0, 2 },
22010 { 0, 0, 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 2 },
22011
22012 /* 481-490 */
22013 { 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2 },
22014 { 0, 0, 0, 0, 0, 0, 0, 3, -8, 3, 0, 0, 0, -2 },
22015 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 1 },
22016 { 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 1 },
22017 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1 },
22018 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1 },
22019 { 2, 0, 0, -2, -1, 0, 0, -6, 8, 0, 0, 0, 0, 0 },
22020 { 2, 0, -1, -1, 1, 0, 0, 3, -7, 0, 0, 0, 0, 0 },
22021 { 0, 0, 2, -2, 1, 0, 0, -7, 9, 0, 0, 0, 0, 0 },
22022 { 0, 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, -1 },
22023
22024 /* 491-500 */
22025 { 0, 0, 1, -1, 2, 0, -8, 12, 0, 0, 0, 0, 0, 0 },
22026 { 1, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
22027 { 1, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0 },
22028 { 0, 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 0, 0 },
22029 { 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0 },
22030 { 2, 0, 0, -2, 1, 0, 0, -5, 6, 0, 0, 0, 0, 0 },
22031 { 2, 0, 0, -2, -1, 0, 0, -2, 0, 3, -1, 0, 0, 0 },
22032 { 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
22033 { 1, 0, 0, -2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
22034 { 1, 0, 0, -2, -1, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
22035
22036 /* 501-510 */
22037 { 1, 0, 0, -1, -1, 0, 0, -3, 4, 0, 0, 0, 0, 0 },
22038 { 1, 0, -1, 0, -1, 0, -3, 5, 0, 0, 0, 0, 0, 0 },
22039 { 0, 0, 2, -2, 1, 0, 0, -4, 4, 0, 0, 0, 0, 0 },
22040 { 0, 0, 2, -2, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0 },
22041 { 0, 0, 2, -2, 1, 0, -8, 11, 0, 0, 0, 0, 0, 0 },
22042 { 0, 0, 2, -2, 0, 0, 0, -9, 13, 0, 0, 0, 0, 0 },
22043 { 0, 0, 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
22044 { 0, 0, 1, -1, 1, 0, 0, 1, -4, 0, 0, 0, 0, 0 },
22045 { 0, 0, 1, -1, 1, 0, 0, -1, 0, 1, -3, 0, 0, 0 },
22046 { 0, 0, 0, 0, 1, 0, 0, 7,-13, 0, 0, 0, 0, 0 },
22047
22048 /* 511-520 */
22049 { 0, 0, 0, 0, 1, 0, 0, 2, 0, -2, 0, 0, 0, 0 },
22050 { 0, 0, 0, 0, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0 },
22051 { 0, 0, 0, 0, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0 },
22052 { 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, 0 },
22053 { 0, 0, 0, 0, 0, 0, 7,-11, 0, 0, 0, 0, 0, -1 },
22054 { 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 1 },
22055 { 0, 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 0, 1 },
22056 { 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, -1 },
22057 { 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0 },
22058 { 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 1 },
22059
22060 /* 521-530 */
22061 { 0, 0, 0, 0, 0, 0, 1, -4, 0, 0, 0, 0, 0, -1 },
22062 { 0, 0, 0, 0, 0, 0, 0, 9,-17, 0, 0, 0, 0, -2 },
22063 { 0, 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 2 },
22064 { 0, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 1 },
22065 { 0, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, -1 },
22066 { 0, 0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, 0 },
22067 { 0, 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, -1 },
22068 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1 },
22069 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0 },
22070 { 2, 0, 0, -2, 0, 0, 0, -4, 8, -3, 0, 0, 0, 0 },
22071
22072 /* 531-540 */
22073 { 2, 0, 0, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0 },
22074 { 1, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0 },
22075 { 1, 0, 0, 0, 0, 0, 0, -4, 8, -3, 0, 0, 0, 0 },
22076 { 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0 },
22077 { 1, 0, 0, -2, 0, 0, 17,-16, 0, -2, 0, 0, 0, 0 },
22078 { 1, 0, 0, -1, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0 },
22079 { 0, 0, 2, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
22080 { 0, 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0 },
22081 { 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0 },
22082 { 0, 0, 0, 0, 0, 0, 0, 3, 0, -4, 0, 0, 0, 0 },
22083
22084 /* 541-550 */
22085 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -2 },
22086 { 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2 },
22087 { 2, 0, 0, -2, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0 },
22088 { 2, 0, 0, -2, 0, 0, 0, -2, 0, 2, 2, 0, 0, 0 },
22089 { 1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0 },
22090 { 1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
22091 { 1, 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
22092 { 1, 0, 0, -2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0 },
22093 { 1, 0, 0, -2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0 },
22094 { 1, 0, 0, -2, 0, 0, 0, -4, 8, -3, 0, 0, 0, 0 },
22095
22096 /* 551-560 */
22097 { 1, 0, 0, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0 },
22098 { 0, 0, 2, -2, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0 },
22099 { 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
22100 { 0, 0, 1, -1, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0 },
22101 { 0, 0, 1, -1, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0 },
22102 { 0, 0, 1, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
22103 { 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0 },
22104 { 0, 0, 1, -1, 0, 0, -4, 5, 0, 0, 0, 0, 0, 0 },
22105 { 0, 0, 1, -1, 0, 0, -3, 4, 0, 0, 0, 0, 0, 0 },
22106 { 0, 0, 0, 2, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
22107
22108 /* 561-570 */
22109 { 0, 0, 0, 0, 0, 0, 8, -9, 0, 0, 0, 0, 0, 0 },
22110 { 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0 },
22111 { 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 },
22112 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0 },
22113 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0 },
22114 { 2, 0, -2, -2, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
22115 { 1, 0, 0, 0, 1, 0,-10, 3, 0, 0, 0, 0, 0, 0 },
22116 { 1, 0, 0, 0, -1, 0,-10, 3, 0, 0, 0, 0, 0, 0 },
22117 { 0, 0, 2, 0, 2, 0, 2, -3, 0, 0, 0, 0, 0, 0 },
22118 { 0, 0, 2, 0, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0 },
22119
22120 /* 571-580 */
22121 { 0, 0, 2, 0, 2, 0, -2, 3, 0, 0, 0, 0, 0, 0 },
22122 { 0, 0, 2, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0 },
22123 { 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0 },
22124 { 0, 0, 0, 0, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0 },
22125 { 2, 0, 2, -2, 2, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
22126 { 2, 0, 1, -3, 1, 0, -6, 7, 0, 0, 0, 0, 0, 0 },
22127 { 2, 0, 0, -2, 0, 0, 2, -5, 0, 0, 0, 0, 0, 0 },
22128 { 2, 0, 0, -2, 0, 0, 0, -2, 0, 5, -5, 0, 0, 0 },
22129 { 2, 0, 0, -2, 0, 0, 0, -2, 0, 1, 5, 0, 0, 0 },
22130 { 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 5, 0, 0, 0 },
22131
22132 /* 581-590 */
22133 { 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0 },
22134 { 2, 0, 0, -2, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0 },
22135 { 2, 0, -2, 0, -2, 0, 0, 5, -9, 0, 0, 0, 0, 0 },
22136 { 2, 0, -1, -1, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0 },
22137 { 1, 0, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0 },
22138 { 1, 0, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0 },
22139 { 1, 0, 2, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0 },
22140 { 1, 0, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0 },
22141 { 1, 0, 2, -2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
22142 { 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0 },
22143
22144 /* 591-600 */
22145 { 1, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
22146 { 1, 0, 0, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0 },
22147 { 1, 0, -2, -2, -2, 0, 0, 1, 0, -1, 0, 0, 0, 0 },
22148 { 1, 0, -1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
22149 { 1, 0, -1, -1, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0 },
22150 { 0, 0, 2, 2, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0 },
22151 { 0, 0, 2, -2, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0 },
22152 { 0, 0, 2, -2, 1, 0, 0, -2, 0, 1, 0, 0, 0, 0 },
22153 { 0, 0, 2, -2, 1, 0, 0,-10, 15, 0, 0, 0, 0, 0 },
22154 { 0, 0, 2, -2, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0 },
22155
22156 /* 601-610 */
22157 { 0, 0, 1, -1, 2, 0, 0, -1, 0, 0, -1, 0, 0, 0 },
22158 { 0, 0, 1, -1, 2, 0, -3, 4, 0, 0, 0, 0, 0, 0 },
22159 { 0, 0, 1, -1, 1, 0, -4, 6, 0, 0, 0, 0, 0, 0 },
22160 { 0, 0, 1, -1, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0 },
22161 { 0, 0, 1, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
22162 { 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0 },
22163 { 0, 0, 1, -1, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0 },
22164 { 0, 0, 1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 },
22165 { 0, 0, 1, -1, -1, 0, -5, 7, 0, 0, 0, 0, 0, 0 },
22166 { 0, 0, 0, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0 },
22167
22168 /* 611-620 */
22169 { 0, 0, 0, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0 },
22170 { 0, 0, 0, 0, 2, 0, -3, 5, 0, 0, 0, 0, 0, 0 },
22171 { 0, 0, 0, 0, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0 },
22172 { 0, 0, 0, 0, 0, 0, 9,-13, 0, 0, 0, 0, 0, -2 },
22173 { 0, 0, 0, 0, 0, 0, 8,-14, 0, 0, 0, 0, 0, -2 },
22174 { 0, 0, 0, 0, 0, 0, 8,-11, 0, 0, 0, 0, 0, -1 },
22175 { 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, 0 },
22176 { 0, 0, 0, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0 },
22177 { 0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 0, -1 },
22178 { 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, -2 },
22179
22180 /* 621-630 */
22181 { 0, 0, 0, 0, 0, 0, 5, -6, -4, 0, 0, 0, 0, -2 },
22182 { 0, 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 0, 2 },
22183 { 0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, 0, -2 },
22184 { 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, 0 },
22185 { 0, 0, 0, 0, 0, 0, 3, -3, 0, 2, 0, 0, 0, 2 },
22186 { 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 0 },
22187 { 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0 },
22188 { 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -2 },
22189 { 0, 0, 0, 0, 0, 0, 0, 7,-12, 0, 0, 0, 0, -2 },
22190 { 0, 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, -2 },
22191
22192 /* 631-640 */
22193 { 0, 0, 0, 0, 0, 0, 0, 6, -8, 1, 5, 0, 0, 2 },
22194 { 0, 0, 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 2 },
22195 { 0, 0, 0, 0, 0, 0, 0, 6,-10, 0, 0, 0, 0, 0 },
22196 { 0, 0, 0, 0, 0, 0, 0, 5, 0, -4, 0, 0, 0, 2 },
22197 { 0, 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, -1 },
22198 { 0, 0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 2 },
22199 { 0, 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, -2 },
22200 { 0, 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0 },
22201 { 0, 0, 0, 0, 0, 0, 0, 5,-16, 4, 5, 0, 0, -2 },
22202 { 0, 0, 0, 0, 0, 0, 0, 5,-13, 0, 0, 0, 0, -2 },
22203
22204 /* 641-650 */
22205 { 0, 0, 0, 0, 0, 0, 0, 3, 0, -5, 0, 0, 0, -2 },
22206 { 0, 0, 0, 0, 0, 0, 0, 3, -9, 0, 0, 0, 0, -2 },
22207 { 0, 0, 0, 0, 0, 0, 0, 3, -7, 0, 0, 0, 0, -2 },
22208 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2 },
22209 { 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -3, 0, 0, 0 },
22210 { 0, 0, 0, 0, 0, 0, 0, 2, -8, 1, 5, 0, 0, -2 },
22211 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -5, 0, 0, 0 },
22212 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2 },
22213 { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -3, 0, 0, 0 },
22214 { 0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 5, 0, 0, 0 },
22215
22216 /* 651-NFPL */
22217 { 0, 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0 },
22218 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -6, 3, 0, -2 },
22219 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0 },
22220 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 },
22221 { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 },
22222 { 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 }
22223 };
22224
22225 /**
22226 *
22227 * Time scale transformation: Terrestrial Time, TT, to International
22228 * Atomic Time, TAI.
22229 *
22230 * <p>This function is derived from the International Astronomical Union's
22231 * SOFA (Standards of Fundamental Astronomy) software collection.
22232 *
22233 *<p>Status: canonical.
22234 *
22235 *<!-- Given: -->
22236 * tt1,tt2 double TT as a 2-part Julian Date
22237 *
22238 *<!-- Returned:-->
22239 * tai1,tai2 double TAI as a 2-part Julian Date
22240 *
22241 * Returned (function value):
22242 * int status: 0 = OK
22243 *
22244 * Note:
22245 *
22246 * tt1+tt2 is Julian Date, apportioned in any convenient way between
22247 * the two arguments, for example where tt1 is the Julian Day Number
22248 * and tt2 is the fraction of a day. The returned tai1,tai2 follow
22249 * suit.
22250 *
22251 *<p>References:
22252 *
22253 * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
22254 * IERS Technical Note No. 32, BKG (2004)
22255 *
22256 * Explanatory Supplement to the Astronomical Almanac,
22257 * P. Kenneth Seidelmann (ed), University Science Books (1992)
22258 *
22259 *@version 2010 May 13
22260 *
22261 *@since SOFA release 2010-12-01
22262 *
22263 * <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
22264 */
22265 public static JulianDate jauTttai(double tt1, double tt2)
22266 {
22267 double tai1, tai2;
22268 /* TT minus TAI (days). */
22269 final double dtat = TTMTAI / 86400.0;
22270
22271
22272 /* Result, safeguarding precision. */
22273 if ( tt1 > tt2 ) {
22274 tai1 = tt1;
22275 tai2 = tt2 - dtat;
22276 } else {
22277 tai1 = tt1 - dtat;
22278 tai2 = tt2;
22279 }
22280
22281 return new JulianDate(tai1, tai2);
22282
22283 };
22284
22285 /**
22286 *
22287 * Time scale transformation: Terrestrial Time, TT, to Geocentric
22288 * Coordinate Time, TCG.
22289 *
22290 * <p>This function is derived from the International Astronomical Union's
22291 * SOFA (Standards of Fundamental Astronomy) software collection.
22292 *
22293 *<p>Status: canonical.
22294 *
22295 *<!-- Given: -->
22296 * tt1,tt2 double TT as a 2-part Julian Date
22297 *
22298 *<!-- Returned:-->
22299 * tcg1,tcg2 double TCG as a 2-part Julian Date
22300 *
22301 * Returned (function value):
22302 * int status: 0 = OK
22303 *
22304 * Note:
22305 *
22306 * tt1+tt2 is Julian Date, apportioned in any convenient way between
22307 * the two arguments, for example where tt1 is the Julian Day Number
22308 * and tt2 is the fraction of a day. The returned tcg1,tcg2 follow
22309 * suit.
22310 *
22311 *<p>References:
22312 *
22313 * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
22314 * IERS Technical Note No. 32, BKG (2004)
22315 *
22316 * IAU 2000 Resolution B1.9
22317 *
22318 *@version 2010 May 13
22319 *
22320 *@since SOFA release 2010-12-01
22321 *
22322 * <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
22323 */
22324 public static JulianDate jauTttcg(double tt1, double tt2)
22325
22326 {
22327 double tcg1, tcg2;
22328
22329 /* 1977 Jan 1 00:00:32.184 TT, as MJD */
22330 final double t77t = DJM77 + TTMTAI/DAYSEC;
22331
22332 /* TT to TCG rate */
22333 final double elgg = ELG/(1.0-ELG);
22334
22335
22336 /* Result, safeguarding precision. */
22337 if ( tt1 > tt2 ) {
22338 tcg1 = tt1;
22339 tcg2 = tt2 + ( ( tt1 - DJM0 ) + ( tt2 - t77t ) ) * elgg;
22340 } else {
22341 tcg1 = tt1 + ( ( tt2 - DJM0 ) + ( tt1 - t77t ) ) * elgg;
22342 tcg2 = tt2;
22343 }
22344
22345 return new JulianDate(tcg1, tcg2);
22346
22347 };
22348
22349 /**
22350 *
22351 * Time scale transformation: Terrestrial Time, TT, to Barycentric
22352 * Dynamical Time, TDB.
22353 *
22354 * <p>This function is derived from the International Astronomical Union's
22355 * SOFA (Standards of Fundamental Astronomy) software collection.
22356 *
22357 *<p>Status: canonical.
22358 *
22359 *<!-- Given: -->
22360 * tt1,tt2 double TT as a 2-part Julian Date
22361 * dtr double TDB-TT in seconds
22362 *
22363 *<!-- Returned:-->
22364 * tdb1,tdb2 double TDB as a 2-part Julian Date
22365 *
22366 * Returned (function value):
22367 * int status: 0 = OK
22368 *
22369 *<p>Notes:
22370 *
22371 * 1 tt1+tt2 is Julian Date, apportioned in any convenient way between
22372 * the two arguments, for example where tt1 is the Julian Day Number
22373 * and tt2 is the fraction of a day. The returned tdb1,tdb2 follow
22374 * suit.
22375 *
22376 * 2 The argument dtr represents the quasi-periodic component of the
22377 * GR transformation between TT and TCB. It is dependent upon the
22378 * adopted solar-system ephemeris, and can be obtained by numerical
22379 * integration, by interrogating a precomputed time ephemeris or by
22380 * evaluating a model such as that implemented in the SOFA function
22381 * jauDtdb. The quantity is dominated by an annual term of 1.7 ms
22382 * amplitude.
22383 *
22384 * 3 TDB is essentially the same as Teph, the time argument for the JPL
22385 * solar system ephemerides.
22386 *
22387 *<p>References:
22388 *
22389 * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
22390 * IERS Technical Note No. 32, BKG (2004)
22391 *
22392 * IAU 2006 Resolution 3
22393 *
22394 *@version 2010 May 13
22395 *
22396 *@since SOFA release 2010-12-01
22397 *
22398 * <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
22399 */
22400 public static JulianDate jauTttdb(double tt1, double tt2, double dtr)
22401 {
22402
22403 double tdb1, tdb2;
22404 double dtrd;
22405
22406
22407 /* Result, safeguarding precision. */
22408 dtrd = dtr / DAYSEC;
22409 if ( tt1 > tt2 ) {
22410 tdb1 = tt1;
22411 tdb2 = tt2 + dtrd;
22412 } else {
22413 tdb1 = tt1 + dtrd;
22414 tdb2 = tt2;
22415 }
22416
22417 return new JulianDate(tdb1, tdb2);
22418
22419 };
22420
22421 /**
22422 *
22423 * Time scale transformation: Terrestrial Time, TT, to Universal Time,
22424 * UT1.
22425 *
22426 * <p>This function is derived from the International Astronomical Union's
22427 * SOFA (Standards of Fundamental Astronomy) software collection.
22428 *
22429 *<p>Status: canonical.
22430 *
22431 *<!-- Given: -->
22432 * tt1,tt2 double TT as a 2-part Julian Date
22433 * dt double TT-UT1 in seconds
22434 *
22435 *<!-- Returned:-->
22436 * ut11,ut12 double UT1 as a 2-part Julian Date
22437 *
22438 * Returned (function value):
22439 * int status: 0 = OK
22440 *
22441 *<p>Notes:
22442 *
22443 * 1 tt1+tt2 is Julian Date, apportioned in any convenient way between
22444 * the two arguments, for example where tt1 is the Julian Day Number
22445 * and tt2 is the fraction of a day. The returned ut11,ut12 follow
22446 * suit.
22447 *
22448 * 2 The argument dt is classical Delta T.
22449 *
22450 * Reference:
22451 *
22452 * Explanatory Supplement to the Astronomical Almanac,
22453 * P. Kenneth Seidelmann (ed), University Science Books (1992)
22454 *
22455 *@version 2010 May 16
22456 *
22457 *@since SOFA release 2010-12-01
22458 *
22459 * <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
22460 */
22461 public static JulianDate jauTtut1(double tt1, double tt2, double dt)
22462
22463 {
22464
22465 double ut11, ut12;
22466 double dtd;
22467
22468
22469 /* Result, safeguarding precision. */
22470 dtd = dt / DAYSEC;
22471 if ( tt1 > tt2 ) {
22472 ut11 = tt1;
22473 ut12 = tt2 - dtd;
22474 } else {
22475 ut11 = tt1 - dtd;
22476 ut12 = tt2;
22477 }
22478
22479 return new JulianDate(ut11, ut12);
22480 };
22481
22482 /**
22483 *
22484 * Time scale transformation: Universal Time, UT1, to International
22485 * Atomic Time, TAI.
22486 *
22487 * <p>This function is derived from the International Astronomical Union's
22488 * SOFA (Standards of Fundamental Astronomy) software collection.
22489 *
22490 *<p>Status: canonical.
22491 *
22492 *<!-- Given: -->
22493 * ut11,ut12 double UT1 as a 2-part Julian Date
22494 * dta double UT1-TAI in seconds
22495 *
22496 *<!-- Returned:-->
22497 * tai1,tai2 double TAI as a 2-part Julian Date
22498 *
22499 * Returned (function value):
22500 * int status: 0 = OK
22501 *
22502 *<p>Notes:
22503 *
22504 * 1 ut11+ut12 is Julian Date, apportioned in any convenient way
22505 * between the two arguments, for example where ut11 is the Julian
22506 * Day Number and ut12 is the fraction of a day. The returned
22507 * TAI1,TAI2 follow suit.
22508 *
22509 * 2 The argument dta, i.e. UT1-TAI, is an observed quantity, and is
22510 * available from IERS tabulations.
22511 *
22512 * Reference:
22513 *
22514 * Explanatory Supplement to the Astronomical Almanac,
22515 * P. Kenneth Seidelmann (ed), University Science Books (1992)
22516 *
22517 *@version 2010 May 16
22518 *
22519 *@since SOFA release 2010-12-01
22520 *
22521 * <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
22522 */
22523 public static JulianDate jauUt1tai(double ut11, double ut12, double dta )
22524
22525 {
22526 double tai1, tai2;
22527 double dtad;
22528
22529
22530 /* Result, safeguarding precision. */
22531 dtad = dta / DAYSEC;
22532 if ( ut11 > ut12 ) {
22533 tai1 = ut11;
22534 tai2 = ut12 - dtad;
22535 } else {
22536 tai1 = ut11 - dtad;
22537 tai2 = ut12;
22538 }
22539 return new JulianDate(tai1, tai2);
22540
22541 };
22542
22543 /**
22544 *
22545 * Time scale transformation: Universal Time, UT1, to Terrestrial
22546 * Time, TT.
22547 *
22548 * <p>This function is derived from the International Astronomical Union's
22549 * SOFA (Standards of Fundamental Astronomy) software collection.
22550 *
22551 *<p>Status: canonical.
22552 *
22553 *<!-- Given: -->
22554 * ut11,ut12 double UT1 as a 2-part Julian Date
22555 * dt double TT-UT1 in seconds
22556 *
22557 *<!-- Returned:-->
22558 * tt1,tt2 double TAI as a 2-part Julian Date
22559 *
22560 * Returned (function value):
22561 * int status: 0 = OK
22562 *
22563 *<p>Notes:
22564 *
22565 * 1 ut11+ut12 is Julian Date, apportioned in any convenient way
22566 * between the two arguments, for example where ut11 is the Julian
22567 * Day Number and ut12 is the fraction of a day. The returned
22568 * tt1,tt2 follow suit.
22569 *
22570 * 2 The argument dt is classical Delta T.
22571 *
22572 * Reference:
22573 *
22574 * Explanatory Supplement to the Astronomical Almanac,
22575 * P. Kenneth Seidelmann (ed), University Science Books (1992)
22576 *
22577 *@version 2010 May 16
22578 *
22579 *@since SOFA release 2010-12-01
22580 *
22581 * <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
22582 */
22583 public static JulianDate jauUt1tt(double ut11, double ut12, double dt)
22584 {
22585
22586 double tt1, tt2;
22587 double dtd;
22588
22589
22590 /* Result, safeguarding precision. */
22591 dtd = dt / DAYSEC;
22592 if ( ut11 > ut12 ) {
22593 tt1 = ut11;
22594 tt2 = ut12 + dtd;
22595 } else {
22596 tt1 = ut11 + dtd;
22597 tt2 = ut12;
22598 }
22599
22600 return new JulianDate(tt1, tt2);
22601
22602 };
22603
22604 /**
22605 *
22606 * Time scale transformation: Universal Time, UT1, to Coordinated
22607 * Universal Time, UTC.
22608 *
22609 * <p>This function is derived from the International Astronomical Union's
22610 * SOFA (Standards of Fundamental Astronomy) software collection.
22611 *
22612 *<p>Status: canonical.
22613 *
22614 *<!-- Given: -->
22615 * @param ut11 double UT1 as a 2-part Julian Date (Note 1)
22616 * @param ut12 double UT1 as a 2-part Julian Date (Note 1)
22617 * dut1 double Delta UT1: UT1-UTC in seconds (Note 2)
22618 *
22619 *<!-- Returned:-->
22620 * @return JulianDate UTC as a 2-part quasi Julian Date (Notes 3,4)
22621 *
22622 * Returned (function value):
22623 * int status: +1 = dubious year (Note 5)
22624 * 0 = OK
22625 * -1 = unacceptable date
22626 *
22627 *<p>Notes:
22628 *<ol>
22629 * <li> ut11+ut12 is Julian Date, apportioned in any convenient way
22630 * between the two arguments, for example where ut11 is the Julian
22631 * Day Number and ut12 is the fraction of a day. The returned utc1
22632 * and utc2 form an analogous pair, except that a special convention
22633 * is used, to deal with the problem of leap seconds - see Note 3.
22634 *
22635 * <li> Delta UT1 can be obtained from tabulations provided by the
22636 * International Earth Rotation and Reference Systems Service. The
22637 * value changes abruptly by 1s at a leap second; however, close to
22638 * a leap second the algorithm used here is tolerant of the "wrong"
22639 * choice of value being made.
22640 *
22641 * <li> JD cannot unambiguously represent UTC during a leap second unless
22642 * special measures are taken. The convention in the present
22643 * function is that the returned quasi JD day UTC1+UTC2 represents
22644 * UTC days whether the length is 86399, 86400 or 86401 SI seconds.
22645 *
22646 * <li> The function jauD2dtf can be used to transform the UTC quasi-JD
22647 * into calendar date and clock time, including UTC leap second
22648 * handling.
22649 *
22650 * <li> The warning status "dubious year" flags UTCs that predate the
22651 * introduction of the time scale and that are too far in the future
22652 * to be trusted. See jauDat for further details.
22653 *</ol>
22654 * Called:
22655 * <ul>
22656 * <li>{@link #jauJd2cal} JD to Gregorian calendar
22657 * <li>{@link #jauDat} delta(AT) = TAI-UTC
22658 * <li>{@link #jauCal2jd} Gregorian calendar to JD
22659 *</ul>
22660 *<p>References:
22661 *
22662 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
22663 * IERS Technical Note No. 32, BKG (2004)
22664 *
22665 * <p>Explanatory Supplement to the Astronomical Almanac,
22666 * P. Kenneth Seidelmann (ed), University Science Books (1992)
22667 *
22668 *@version 2010 May 16
22669 *
22670 *@since SOFA release 2010-12-01
22671 *
22672 * <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
22673 * @throws JSOFAIllegalParameter
22674 * @throws JSOFAInternalError
22675 */
22676 public static JulianDate jauUt1utc(double ut11, double ut12, double dut1) throws JSOFAIllegalParameter, JSOFAInternalError
22677
22678 {
22679
22680 double utc1, utc2;
22681 boolean big1;
22682 int i;
22683 double duts, u1, u2, d1, dats1, d2, fd, dats2, ddats, us1, us2, du;
22684
22685
22686 /* UT1-UTC in seconds. */
22687 duts = dut1;
22688
22689 /* Put the two parts of the UT1 into big-first order. */
22690 big1 = ( ut11 >= ut12 );
22691 if ( big1 ) {
22692 u1 = ut11;
22693 u2 = ut12;
22694 } else {
22695 u1 = ut12;
22696 u2 = ut11;
22697 }
22698
22699 /* See if the UT1 can possibly be in a leap-second day. */
22700 d1 = u1;
22701 dats1 = 0;
22702 for ( i = -1; i <= 3; i++ ) {
22703 d2 = u2 + (double) i;
22704 Calendar dt = jauJd2cal(d1, d2 );
22705 dats2 = jauDat(dt.iy, dt.im, dt.id, 0.0);
22706 if ( i == - 1 ) dats1 = dats2;
22707 ddats = dats2 - dats1;
22708 if ( abs(ddats) >= 0.5 ) {
22709
22710 /* Yes, leap second nearby: ensure UT1-UTC is "before" value. */
22711 if ( ddats * duts >= 0 ) duts -= ddats;
22712
22713 /* UT1 for the start of the UTC day that ends in a leap. */
22714 JulianDate jd = jauCal2jd(dt.iy, dt.im, dt.id );
22715 d1 = jd.djm0; d2 = jd.djm1;
22716 us1 = d1;
22717 us2 = d2 - 1.0 + duts/DAYSEC;
22718
22719 /* Is the UT1 after this point? */
22720 du = u1 - us1;
22721 du += u2 - us2;
22722 if ( du > 0 ) {
22723
22724 /* Yes: fraction of the current UTC day that has elapsed. */
22725 fd = du * DAYSEC / ( DAYSEC + ddats );
22726
22727 /* Ramp UT1-UTC to bring about SOFA's JD(UTC) convention. */
22728 duts += ddats * ( fd <= 1.0 ? fd : 1.0 );
22729 }
22730
22731 /* Done. */
22732 break;
22733 }
22734 dats1 = dats2;
22735 }
22736
22737 /* Subtract the (possibly adjusted) UT1-UTC from UT1 to give UTC. */
22738 u2 -= duts / DAYSEC;
22739
22740 /* Result, safeguarding precision. */
22741 if ( big1 ) {
22742 utc1 = u1;
22743 utc2 = u2;
22744 } else {
22745 utc1 = u2;
22746 utc2 = u1;
22747 }
22748
22749 /* FIXME Status. */
22750 return new JulianDate(utc1, utc2);
22751
22752 };
22753
22754 /**
22755 *
22756 * Time scale transformation: Coordinated Universal Time, UTC, to
22757 * International Atomic Time, TAI.
22758 *
22759 * <p>This function is derived from the International Astronomical Union's
22760 * SOFA (Standards of Fundamental Astronomy) software collection.
22761 *
22762 *<p>Status: canonical.
22763 *
22764 *<!-- Given: -->
22765 * @param utc1 double UTC as a 2-part quasi Julian Date (Notes 1-4)
22766 * @param utc2 double UTC as a 2-part quasi Julian Date (Notes 1-4)
22767 *
22768 *<!-- Returned:-->
22769 * @return JulianDate TAI as a 2-part Julian Date (Note 5)
22770 *
22771 * Returned (function value):
22772 * int status: +1 = dubious year (Note 3)
22773 * 0 = OK
22774 * -1 = unacceptable date
22775 *
22776 *<p>Notes:
22777 *<ol>
22778 * <li> utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
22779 * convenient way between the two arguments, for example where utc1
22780 * is the Julian Day Number and utc2 is the fraction of a day.
22781 *
22782 * <li> JD cannot unambiguously represent UTC during a leap second unless
22783 * special measures are taken. The convention in the present
22784 * function is that the JD day represents UTC days whether the
22785 * length is 86399, 86400 or 86401 SI seconds.
22786 *
22787 * <li> The warning status "dubious year" flags UTCs that predate the
22788 * introduction of the time scale and that are too far in the future
22789 * to be trusted. See jauDat for further details.
22790 *
22791 * <li> The function jauDtf2d converts from calendar date and time of day
22792 * into 2-part Julian Date, and in the case of UTC implements the
22793 * leap-second-ambiguity convention described above.
22794 *
22795 * <li> The returned TAI1,TAI2 are such that their sum is the TAI Julian
22796 * Date.
22797 *</ol>
22798 * Called:<ul>
22799 * <li>{@link #jauJd2cal} JD to Gregorian calendar
22800 * <li>{@link #jauDat} delta(AT) = TAI-UTC
22801 * <li>{@link #jauCal2jd} Gregorian calendar to JD
22802 *</ul>
22803 *<p>References:
22804 *
22805 * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
22806 * IERS Technical Note No. 32, BKG (2004)
22807 *
22808 * Explanatory Supplement to the Astronomical Almanac,
22809 * P. Kenneth Seidelmann (ed), University Science Books (1992)
22810 *
22811 *@version 2010 September 10
22812 *
22813 *@since SOFA release 2010-12-01
22814 *
22815 * <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
22816 * @throws JSOFAInternalError
22817 * @throws JSOFAIllegalParameter
22818 *
22819 */
22820 public static JulianDate jauUtctai(double utc1, double utc2) throws JSOFAIllegalParameter, JSOFAInternalError
22821
22822 {
22823 double tai1, tai2;
22824 boolean big1;
22825 double u1, u2, dats, datst, ddat, a2, fd;
22826
22827
22828 /* Put the two parts of the UTC into big-first order. */
22829 big1 = ( utc1 >= utc2 );
22830 if ( big1 ) {
22831 u1 = utc1;
22832 u2 = utc2;
22833 } else {
22834 u1 = utc2;
22835 u2 = utc1;
22836 }
22837
22838 /* Get TAI-UTC now. */
22839 Calendar dt = jauJd2cal(u1, u2 );
22840 dats = jauDat(dt.iy, dt.im, dt.id, dt.fd);
22841 // if ( js < 0 ) return -1;
22842 fd = dt.fd;
22843 /* Get TAI-UTC tomorrow. */
22844 Calendar dtt = jauJd2cal(u1+1.5, u2-fd );
22845 datst = jauDat(dtt.iy, dtt.im, dtt.id, dtt.fd);
22846 // if ( js < 0 ) return -1;
22847
22848 /* If today ends in a leap second, scale the fraction into SI days. */
22849 ddat = datst - dats;
22850 if ( abs(ddat) > 0.5 ) fd += fd * ddat / DAYSEC;
22851
22852 /* Today's calendar date to 2-part JD. */
22853 JulianDate jd = jauCal2jd(dt.iy, dt.im, dt.id ) ;
22854
22855 /* Assemble the TAI result, preserving the UTC split and order. */
22856 a2 = jd.djm0 - u1;
22857 a2 += jd.djm1;
22858 a2 += fd + dats / DAYSEC;
22859 if ( big1 ) {
22860 tai1 = u1;
22861 tai2 = a2;
22862 } else {
22863 tai1 = a2;
22864 tai2 = u1;
22865 }
22866
22867 /* FIXME Status. */
22868 return new JulianDate(tai1, tai2);
22869
22870 };
22871
22872 /**
22873 *
22874 * Time scale transformation: Coordinated Universal Time, UTC, to
22875 * Universal Time, UT1.
22876 *
22877 * <p>This function is derived from the International Astronomical Union's
22878 * SOFA (Standards of Fundamental Astronomy) software collection.
22879 *
22880 *<p>Status: canonical.
22881 *
22882 *<!-- Given: -->
22883 * utc1,utc2 double UTC as a 2-part quasi Julian Date (Notes 1-4)
22884 * dut1 double Delta UT1 = UT1-UTC in seconds (Note 5)
22885 *
22886 *<!-- Returned:-->
22887 * ut11,ut12 double UT1 as a 2-part Julian Date (Note 6)
22888 *
22889 * Returned (function value):
22890 * int status: +1 = dubious year (Note 7)
22891 * 0 = OK
22892 * -1 = unacceptable date
22893 *
22894 *<p>Notes:
22895 *<ol>
22896 * <li> utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
22897 * convenient way between the two arguments, for example where utc1
22898 * is the Julian Day Number and utc2 is the fraction of a day.
22899 *
22900 * <li> JD cannot unambiguously represent UTC during a leap second unless
22901 * special measures are taken. The convention in the present
22902 * function is that the JD day represents UTC days whether the
22903 * length is 86399, 86400 or 86401 SI seconds.
22904 *
22905 * <li> The warning status "dubious year" flags UTCs that predate the
22906 * introduction of the time scale and that are too far in the future
22907 * to be trusted. See jauDat for further details.
22908 *
22909 * <li> The function jauDtf2d converts from calendar date and time of
22910 * day into 2-part Julian Date, and in the case of UTC implements
22911 * the leap-second-ambiguity convention described above.
22912 *
22913 * <li> Delta UT1 can be obtained from tabulations provided by the
22914 * International Earth Rotation and Reference Systems Service. It
22915 * It is the caller's responsibility to supply a DUT argument
22916 * containing the UT1-UTC value that matches the given UTC.
22917 *
22918 * <li> The returned ut11,ut12 are such that their sum is the UT1 Julian
22919 * Date.
22920 *
22921 * <li> The warning status "dubious year" flags UTCs that predate the
22922 * introduction of the time scale and that are too far in the future
22923 * to be trusted. See jauDat for further details.
22924 *</ol>
22925 *<p>References:
22926 *
22927 * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
22928 * IERS Technical Note No. 32, BKG (2004)
22929 *
22930 * Explanatory Supplement to the Astronomical Almanac,
22931 * P. Kenneth Seidelmann (ed), University Science Books (1992)
22932 *
22933 * Called:<ul>
22934 * <li>{@link #jauJd2cal} JD to Gregorian calendar
22935 * <li>{@link #jauDat} delta(AT) = TAI-UTC
22936 * <li>{@link #jauUtctai} UTC to TAI
22937 * <li>{@link #jauTaiut1} TAI to UT1
22938 *</ul>
22939 *@version 2010 May 16
22940 *
22941 *@since SOFA release 2010-12-01
22942 *
22943 * <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
22944 * @throws JSOFAInternalError
22945 * @throws JSOFAIllegalParameter
22946 */
22947 public static JulianDate jauUtcut1(double utc1, double utc2, double dut1) throws JSOFAIllegalParameter, JSOFAInternalError
22948 {
22949
22950
22951 double dta;
22952 /* Look up TAI-UTC. */
22953 Calendar dt = jauJd2cal(utc1, utc2) ;
22954 double dat = jauDat ( dt.iy, dt.im, dt.id, 0.0 );
22955
22956
22957 /* Form UT1-TAI. */
22958 dta = dut1 - dat;
22959
22960 /* UTC to TAI to UT1. */
22961 JulianDate tai = jauUtctai(utc1, utc2);
22962 return jauTaiut1(tai.djm0, tai.djm1, dta) ;
22963
22964 };
22965
22966
22967 public static CelestialIntermediatePole jauXy06(double date1, double date2)
22968 /**
22969 * X,Y coordinates of celestial intermediate pole from series based
22970 * on IAU 2006 precession and IAU 2000A nutation.
22971 *
22972 *<p>This function is derived from the International Astronomical Union's
22973 * SOFA (Standards Of Fundamental Astronomy) software collection.
22974 *
22975 *<p>Status: canonical model.
22976 *
22977 *<!-- Given: -->
22978 * @param date1 double TT as a 2-part Julian Date (Note 1)
22979 * @param date2 double TT as a 2-part Julian Date (Note 1)
22980 *
22981 *<!-- Returned: -->
22982 * @return CIP X,Y coordinates (Note 2)
22983 *
22984 * <p>Notes:
22985 * <ol>
22986 *
22987 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
22988 * convenient way between the two arguments. For example,
22989 * JD(TT)=2450123.7 could be expressed in any of these ways,
22990 * among others:
22991 *<pre>
22992 * date1 date2
22993 *
22994 * 2450123.7 0.0 (JD method)
22995 * 2451545.0 -1421.3 (J2000 method)
22996 * 2400000.5 50123.2 (MJD method)
22997 * 2450123.5 0.2 (date & time method)
22998 *</pre>
22999 * The JD method is the most natural and convenient to use in
23000 * cases where the loss of several decimal digits of resolution
23001 * is acceptable. The J2000 method is best matched to the way
23002 * the argument is handled internally and will deliver the
23003 * optimum resolution. The MJD method and the date & time methods
23004 * are both good compromises between resolution and convenience.
23005 *
23006 * <li> The X,Y coordinates are those of the unit vector towards the
23007 * celestial intermediate pole. They represent the combined effects
23008 * of frame bias, precession and nutation.
23009 *
23010 * <li> The fundamental arguments used are as adopted in IERS Conventions
23011 * (2003) and are from Simon et al. (1994) and Souchay et al.
23012 * (1999).
23013 *
23014 * <li> This is an alternative to the angles-based method, via the JSOFA
23015 * function jauFw2xy and as used in jauXys06a for example. The two
23016 * methods agree at the 1 microarcsecond level (at present), a
23017 * negligible amount compared with the intrinsic accuracy of the
23018 * models. However, it would be unwise to mix the two methods
23019 * (angles-based and series-based) in a single application.
23020 *</ol>
23021 *<p>Called:<ul>
23022 * <li>{@link #jauFal03} mean anomaly of the Moon
23023 * <li>{@link #jauFalp03} mean anomaly of the Sun
23024 * <li>{@link #jauFaf03} mean argument of the latitude of the Moon
23025 * <li>{@link #jauFad03} mean elongation of the Moon from the Sun
23026 * <li>{@link #jauFaom03} mean longitude of the Moon's ascending node
23027 * <li>{@link #jauFame03} mean longitude of Mercury
23028 * <li>{@link #jauFave03} mean longitude of Venus
23029 * <li>{@link #jauFae03} mean longitude of Earth
23030 * <li>{@link #jauFama03} mean longitude of Mars
23031 * <li>{@link #jauFaju03} mean longitude of Jupiter
23032 * <li>{@link #jauFasa03} mean longitude of Saturn
23033 * <li>{@link #jauFaur03} mean longitude of Uranus
23034 * <li>{@link #jauFane03} mean longitude of Neptune
23035 * <li>{@link #jauFapa03} general accumulated precession in longitude
23036 * </ul>
23037 *<p>References:
23038 *
23039 * <p>Capitaine, N., Wallace, P.T. & Chapront, J., 2003,
23040 * Astron.Astrophys., 412, 567
23041 *
23042 * <p>Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
23043 *
23044 * <p>McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
23045 * IERS Technical Note No. 32, BKG
23046 *
23047 * Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
23048 * Francou, G. & Laskar, J., Astron.Astrophys., 1994, 282, 663
23049 *
23050 * Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M., 1999,
23051 * Astron.Astrophys.Supp.Ser. 135, 111
23052 *
23053 * <p>Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
23054 *
23055 *@version 2009 October 16
23056 *
23057 * @since Release 20101201
23058 *
23059 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
23060 */
23061 {
23062
23063 /* Maximum power of T in the polynomials for X and Y */
23064 final int MAXPT = (5);
23065
23066 /* Polynomial coefficients (arcsec, X then Y). */
23067 final double xyp[][] = {
23068
23069 { -0.016617,
23070 2004.191898,
23071 -0.4297829,
23072 -0.19861834,
23073 0.000007578,
23074 0.0000059285
23075 },
23076 { -0.006951,
23077 -0.025896,
23078 -22.4072747,
23079 0.00190059,
23080 0.001112526,
23081 0.0000001358
23082 }
23083 };
23084
23085 /* N.B mfals defined as class static (outside this method) to avoid problems with 65535 byte limit for methods */
23086 /* Number of frequencies: luni-solar */
23087 final int NFLS = mfals.length;
23088
23089 /* Number of frequencies: planetary */
23090 final int NFPL =mfapl.length ;
23091
23092 /* Pointers into amplitudes array, one pointer per frequency */
23093 final int nc[] = {
23094
23095 /* 1-100 */
23096 1, 21, 37, 51, 65, 79, 91, 103, 115, 127,
23097 139, 151, 163, 172, 184, 196, 207, 219, 231, 240,
23098 252, 261, 273, 285, 297, 309, 318, 327, 339, 351,
23099 363, 372, 384, 396, 405, 415, 423, 435, 444, 452,
23100 460, 467, 474, 482, 490, 498, 506, 513, 521, 528,
23101 536, 543, 551, 559, 566, 574, 582, 590, 597, 605,
23102 613, 620, 628, 636, 644, 651, 658, 666, 674, 680,
23103 687, 695, 702, 710, 717, 725, 732, 739, 746, 753,
23104 760, 767, 774, 782, 790, 798, 805, 812, 819, 826,
23105 833, 840, 846, 853, 860, 867, 874, 881, 888, 895,
23106
23107 /* 101-200 */
23108 901, 908, 914, 921, 928, 934, 941, 948, 955, 962,
23109 969, 976, 982, 989, 996, 1003, 1010, 1017, 1024, 1031,
23110 1037, 1043, 1050, 1057, 1064, 1071, 1078, 1084, 1091, 1098,
23111 1104, 1112, 1118, 1124, 1131, 1138, 1145, 1151, 1157, 1164,
23112 1171, 1178, 1185, 1192, 1199, 1205, 1212, 1218, 1226, 1232,
23113 1239, 1245, 1252, 1259, 1266, 1272, 1278, 1284, 1292, 1298,
23114 1304, 1310, 1316, 1323, 1329, 1335, 1341, 1347, 1353, 1359,
23115 1365, 1371, 1377, 1383, 1389, 1396, 1402, 1408, 1414, 1420,
23116 1426, 1434, 1440, 1446, 1452, 1459, 1465, 1471, 1477, 1482,
23117 1488, 1493, 1499, 1504, 1509, 1514, 1520, 1527, 1532, 1538,
23118
23119 /* 201-300 */
23120 1543, 1548, 1553, 1558, 1564, 1569, 1574, 1579, 1584, 1589,
23121 1594, 1596, 1598, 1600, 1602, 1605, 1608, 1610, 1612, 1617,
23122 1619, 1623, 1625, 1627, 1629, 1632, 1634, 1640, 1642, 1644,
23123 1646, 1648, 1650, 1652, 1654, 1658, 1660, 1662, 1664, 1668,
23124 1670, 1672, 1673, 1675, 1679, 1681, 1683, 1684, 1686, 1688,
23125 1690, 1693, 1695, 1697, 1701, 1703, 1705, 1707, 1709, 1711,
23126 1712, 1715, 1717, 1721, 1723, 1725, 1727, 1729, 1731, 1733,
23127 1735, 1737, 1739, 1741, 1743, 1745, 1747, 1749, 1751, 1753,
23128 1755, 1757, 1759, 1761, 1762, 1764, 1766, 1768, 1769, 1771,
23129 1773, 1775, 1777, 1779, 1781, 1783, 1785, 1787, 1788, 1790,
23130
23131 /* 301-400 */
23132 1792, 1794, 1796, 1798, 1800, 1802, 1804, 1806, 1807, 1809,
23133 1811, 1815, 1817, 1819, 1821, 1823, 1825, 1827, 1829, 1831,
23134 1833, 1835, 1837, 1839, 1840, 1842, 1844, 1848, 1850, 1852,
23135 1854, 1856, 1858, 1859, 1860, 1862, 1864, 1866, 1868, 1869,
23136 1871, 1873, 1875, 1877, 1879, 1881, 1883, 1885, 1887, 1889,
23137 1891, 1892, 1896, 1898, 1900, 1901, 1903, 1905, 1907, 1909,
23138 1910, 1911, 1913, 1915, 1919, 1921, 1923, 1927, 1929, 1931,
23139 1933, 1935, 1937, 1939, 1943, 1945, 1947, 1948, 1949, 1951,
23140 1953, 1955, 1957, 1958, 1960, 1962, 1964, 1966, 1968, 1970,
23141 1971, 1973, 1974, 1975, 1977, 1979, 1980, 1981, 1982, 1984,
23142
23143 /* 401-500 */
23144 1986, 1988, 1990, 1992, 1994, 1995, 1997, 1999, 2001, 2003,
23145 2005, 2007, 2008, 2009, 2011, 2013, 2015, 2017, 2019, 2021,
23146 2023, 2024, 2025, 2027, 2029, 2031, 2033, 2035, 2037, 2041,
23147 2043, 2045, 2046, 2047, 2049, 2051, 2053, 2055, 2056, 2057,
23148 2059, 2061, 2063, 2065, 2067, 2069, 2070, 2071, 2072, 2074,
23149 2076, 2078, 2080, 2082, 2084, 2086, 2088, 2090, 2092, 2094,
23150 2095, 2096, 2097, 2099, 2101, 2105, 2106, 2107, 2108, 2109,
23151 2110, 2111, 2113, 2115, 2119, 2121, 2123, 2125, 2127, 2129,
23152 2131, 2133, 2135, 2136, 2137, 2139, 2141, 2143, 2145, 2147,
23153 2149, 2151, 2153, 2155, 2157, 2159, 2161, 2163, 2165, 2167,
23154
23155 /* 501-600 */
23156 2169, 2171, 2173, 2175, 2177, 2179, 2181, 2183, 2185, 2186,
23157 2187, 2188, 2192, 2193, 2195, 2197, 2199, 2201, 2203, 2205,
23158 2207, 2209, 2211, 2213, 2217, 2219, 2221, 2223, 2225, 2227,
23159 2229, 2231, 2233, 2234, 2235, 2236, 2237, 2238, 2239, 2240,
23160 2241, 2244, 2246, 2248, 2250, 2252, 2254, 2256, 2258, 2260,
23161 2262, 2264, 2266, 2268, 2270, 2272, 2274, 2276, 2278, 2280,
23162 2282, 2284, 2286, 2288, 2290, 2292, 2294, 2296, 2298, 2300,
23163 2302, 2303, 2304, 2305, 2306, 2307, 2309, 2311, 2313, 2315,
23164 2317, 2319, 2321, 2323, 2325, 2327, 2329, 2331, 2333, 2335,
23165 2337, 2341, 2343, 2345, 2347, 2349, 2351, 2352, 2355, 2356,
23166
23167 /* 601-700 */
23168 2357, 2358, 2359, 2361, 2363, 2364, 2365, 2366, 2367, 2368,
23169 2369, 2370, 2371, 2372, 2373, 2374, 2376, 2378, 2380, 2382,
23170 2384, 2385, 2386, 2387, 2388, 2389, 2390, 2391, 2392, 2393,
23171 2394, 2395, 2396, 2397, 2398, 2399, 2400, 2401, 2402, 2403,
23172 2404, 2405, 2406, 2407, 2408, 2409, 2410, 2411, 2412, 2413,
23173 2414, 2415, 2417, 2418, 2430, 2438, 2445, 2453, 2460, 2468,
23174 2474, 2480, 2488, 2496, 2504, 2512, 2520, 2527, 2535, 2543,
23175 2550, 2558, 2566, 2574, 2580, 2588, 2596, 2604, 2612, 2619,
23176 2627, 2634, 2642, 2648, 2656, 2664, 2671, 2679, 2685, 2693,
23177 2701, 2709, 2717, 2725, 2733, 2739, 2747, 2753, 2761, 2769,
23178
23179 /* 701-800 */
23180 2777, 2785, 2793, 2801, 2809, 2817, 2825, 2833, 2841, 2848,
23181 2856, 2864, 2872, 2878, 2884, 2892, 2898, 2906, 2914, 2922,
23182 2930, 2938, 2944, 2952, 2958, 2966, 2974, 2982, 2988, 2996,
23183 3001, 3009, 3017, 3025, 3032, 3039, 3045, 3052, 3059, 3067,
23184 3069, 3076, 3083, 3090, 3098, 3105, 3109, 3111, 3113, 3120,
23185 3124, 3128, 3132, 3136, 3140, 3144, 3146, 3150, 3158, 3161,
23186 3165, 3166, 3168, 3172, 3176, 3180, 3182, 3185, 3189, 3193,
23187 3194, 3197, 3200, 3204, 3208, 3212, 3216, 3219, 3221, 3222,
23188 3226, 3230, 3234, 3238, 3242, 3243, 3247, 3251, 3254, 3258,
23189 3262, 3266, 3270, 3274, 3275, 3279, 3283, 3287, 3289, 3293,
23190
23191 /* 801-900 */
23192 3296, 3300, 3303, 3307, 3311, 3315, 3319, 3321, 3324, 3327,
23193 3330, 3334, 3338, 3340, 3342, 3346, 3350, 3354, 3358, 3361,
23194 3365, 3369, 3373, 3377, 3381, 3385, 3389, 3393, 3394, 3398,
23195 3402, 3406, 3410, 3413, 3417, 3421, 3425, 3429, 3433, 3435,
23196 3439, 3443, 3446, 3450, 3453, 3457, 3458, 3461, 3464, 3468,
23197 3472, 3476, 3478, 3481, 3485, 3489, 3493, 3497, 3501, 3505,
23198 3507, 3511, 3514, 3517, 3521, 3524, 3525, 3527, 3529, 3533,
23199 3536, 3540, 3541, 3545, 3548, 3551, 3555, 3559, 3563, 3567,
23200 3569, 3570, 3574, 3576, 3578, 3582, 3586, 3590, 3593, 3596,
23201 3600, 3604, 3608, 3612, 3616, 3620, 3623, 3626, 3630, 3632,
23202
23203 /* 901-1000 */
23204 3636, 3640, 3643, 3646, 3648, 3652, 3656, 3660, 3664, 3667,
23205 3669, 3671, 3675, 3679, 3683, 3687, 3689, 3693, 3694, 3695,
23206 3699, 3703, 3705, 3707, 3710, 3713, 3717, 3721, 3725, 3729,
23207 3733, 3736, 3740, 3744, 3748, 3752, 3754, 3757, 3759, 3763,
23208 3767, 3770, 3773, 3777, 3779, 3783, 3786, 3790, 3794, 3798,
23209 3801, 3805, 3809, 3813, 3817, 3821, 3825, 3827, 3831, 3835,
23210 3836, 3837, 3840, 3844, 3848, 3852, 3856, 3859, 3863, 3867,
23211 3869, 3871, 3875, 3879, 3883, 3887, 3890, 3894, 3898, 3901,
23212 3905, 3909, 3913, 3917, 3921, 3922, 3923, 3924, 3926, 3930,
23213 3932, 3936, 3938, 3940, 3944, 3948, 3952, 3956, 3959, 3963,
23214
23215 /* 1001-1100 */
23216 3965, 3969, 3973, 3977, 3979, 3981, 3982, 3986, 3989, 3993,
23217 3997, 4001, 4004, 4006, 4009, 4012, 4016, 4020, 4024, 4026,
23218 4028, 4032, 4036, 4040, 4044, 4046, 4050, 4054, 4058, 4060,
23219 4062, 4063, 4064, 4068, 4071, 4075, 4077, 4081, 4083, 4087,
23220 4089, 4091, 4095, 4099, 4101, 4103, 4105, 4107, 4111, 4115,
23221 4119, 4123, 4127, 4129, 4131, 4135, 4139, 4141, 4143, 4145,
23222 4149, 4153, 4157, 4161, 4165, 4169, 4173, 4177, 4180, 4183,
23223 4187, 4191, 4195, 4198, 4201, 4205, 4209, 4212, 4213, 4216,
23224 4217, 4221, 4223, 4226, 4230, 4234, 4236, 4240, 4244, 4248,
23225 4252, 4256, 4258, 4262, 4264, 4266, 4268, 4270, 4272, 4276,
23226
23227 /* 1101-1200 */
23228 4279, 4283, 4285, 4287, 4289, 4293, 4295, 4299, 4300, 4301,
23229 4305, 4309, 4313, 4317, 4319, 4323, 4325, 4329, 4331, 4333,
23230 4335, 4337, 4341, 4345, 4349, 4351, 4353, 4357, 4361, 4365,
23231 4367, 4369, 4373, 4377, 4381, 4383, 4387, 4389, 4391, 4395,
23232 4399, 4403, 4407, 4411, 4413, 4414, 4415, 4418, 4419, 4421,
23233 4423, 4427, 4429, 4431, 4433, 4435, 4437, 4439, 4443, 4446,
23234 4450, 4452, 4456, 4458, 4460, 4462, 4466, 4469, 4473, 4477,
23235 4481, 4483, 4487, 4489, 4491, 4493, 4497, 4499, 4501, 4504,
23236 4506, 4510, 4513, 4514, 4515, 4518, 4521, 4522, 4525, 4526,
23237 4527, 4530, 4533, 4534, 4537, 4541, 4542, 4543, 4544, 4545,
23238
23239 /* 1201-1300 */
23240 4546, 4547, 4550, 4553, 4554, 4555, 4558, 4561, 4564, 4567,
23241 4568, 4571, 4574, 4575, 4578, 4581, 4582, 4585, 4586, 4588,
23242 4590, 4592, 4596, 4598, 4602, 4604, 4608, 4612, 4613, 4616,
23243 4619, 4622, 4623, 4624, 4625, 4626, 4629, 4632, 4633, 4636,
23244 4639, 4640, 4641, 4642, 4643, 4644, 4645, 4648, 4649, 4650,
23245 4651, 4652, 4653, 4656, 4657, 4660, 4661, 4664, 4667, 4670,
23246 4671, 4674, 4675, 4676, 4677, 4678, 4681, 4682, 4683, 4684,
23247 4687, 4688, 4689, 4692, 4693, 4696, 4697, 4700, 4701, 4702,
23248 4703, 4704, 4707, 4708, 4711, 4712, 4715, 4716, 4717, 4718,
23249 4719, 4720, 4721, 4722, 4723, 4726, 4729, 4730, 4733, 4736,
23250
23251 /* 1301-(NFLS+NFPL) */
23252 4737, 4740, 4741, 4742, 4745, 4746, 4749, 4752, 4753
23253 };
23254
23255 /* Amplitude coefficients (microarcsec); indexed using the nc array. */
23256 final double a[] = {
23257
23258 /* 1-105 */
23259 -6844318.44, 9205236.26,1328.67,1538.18, 205833.11,
23260 153041.79, -3309.73, 853.32,2037.98, -2301.27,
23261 81.46, 120.56, -20.39, -15.22, 1.73, -1.61, -0.10, 0.11,
23262 -0.02, -0.02, -523908.04, 573033.42,-544.75,-458.66,
23263 12814.01, 11714.49, 198.97,-290.91, 155.74,-143.27,
23264 -2.75, -1.03, -1.27, -1.16, 0.00, -0.01, -90552.22,
23265 97846.69, 111.23, 137.41,2187.91,2024.68, 41.44, -51.26,
23266 26.92, -24.46, -0.46, -0.28, -0.22, -0.20, 82168.76,
23267 -89618.24, -27.64, -29.05, -2004.36, -1837.32,
23268 -36.07, 48.00, -24.43, 22.41, 0.47, 0.24, 0.20, 0.18,
23269 58707.02,7387.02, 470.05,-192.40, 164.33, -1312.21,
23270 -179.73, -28.93, -17.36, -1.83, -0.50, 3.57, 0.00, 0.13,
23271 -20557.78, 22438.42, -20.84, -17.40, 501.82, 459.68,
23272 59.20, -67.30, 6.08, -5.61, -1.36, -1.19, 28288.28,
23273 -674.99, -34.69, 35.80, -15.07,-632.54, -11.19, 0.78, -8.41,
23274 0.17, 0.01, 0.07, -15406.85, 20069.50, 15.12,
23275
23276 /* 106-219 */
23277 31.80, 448.76, 344.50, -5.77, 1.41, 4.59, -5.02, 0.17,
23278 0.24, -11991.74, 12902.66, 32.46, 36.70, 288.49,
23279 268.14, 5.70, -7.06, 3.57, -3.23, -0.06, -0.04,
23280 -8584.95, -9592.72, 4.42, -13.20,-214.50, 192.06,
23281 23.87, 29.83, 2.54, 2.40, 0.60, -0.48,5095.50,
23282 -6918.22, 7.19, 3.92,-154.91,-113.94, 2.86, -1.04,
23283 -1.52, 1.73, -0.07, -0.10, -4910.93, -5331.13,
23284 0.76, 0.40,-119.21, 109.81, 2.16, 3.20, 1.46, 1.33,
23285 0.04, -0.02, -6245.02,-123.48, -6.68, -8.20, -2.76,
23286 139.64, 2.71, 0.15, 1.86,2511.85, -3323.89, 1.07,
23287 -0.90, -74.33, -56.17, 1.16, -0.01, -0.75, 0.83, -0.02,
23288 -0.04,2307.58,3143.98, -7.52, 7.50, 70.31, -51.60, 1.46,
23289 0.16, -0.69, -0.79, 0.02, -0.05,2372.58,2554.51, 5.93,
23290 -6.60, 57.12, -53.05, -0.96, -1.24, -0.71, -0.64, -0.01,
23291 -2053.16,2636.13, 5.13, 7.80, 58.94, 45.91, -0.42,
23292 -0.12, 0.61, -0.66, 0.02, 0.03, -1825.49,
23293
23294 /* 220-339 */
23295 -2423.59, 1.23, -2.00, -54.19, 40.82, -1.07, -1.02,
23296 0.54, 0.61, -0.04, 0.04,2521.07,-122.28, -5.97, 2.90,
23297 -2.73, -56.37, -0.82, 0.13, -0.75, -1534.09,1645.01,
23298 6.29, 6.80, 36.78, 34.30, 0.92, -1.25, 0.46, -0.41,
23299 -0.02, -0.01,1898.27, 47.70, -0.72, 2.50, 1.07, -42.45,
23300 -0.94, 0.02, -0.56, -1292.02, -1387.00, 0.00,
23301 0.00, -31.01, 28.89, 0.68, 0.00, 0.38, 0.35, -0.01,
23302 -0.01, -1234.96,1323.81, 5.21, 5.90, 29.60, 27.61,
23303 0.74, -1.22, 0.37, -0.33, -0.02, -0.01,1137.48,
23304 -1233.89, -0.04, -0.30, -27.59, -25.43, -0.61, 1.00,
23305 -0.34, 0.31, 0.01, 0.01,-813.13, -1075.60, 0.40,
23306 0.30, -24.05, 18.18, -0.40, -0.01, 0.24, 0.27, -0.01,
23307 0.01,1163.22, -60.90, -2.94, 1.30, -1.36, -26.01, -0.58,
23308 0.07, -0.35,1029.70, -55.55, -2.63, 1.10, -1.25, -23.02,
23309 -0.52, 0.06, -0.31,-556.26, 852.85, 3.16, -4.48, 19.06,
23310 12.44, -0.81, -0.27, 0.17, -0.21, 0.00, 0.02,-603.52,
23311
23312 /* 340-467 */
23313 -800.34, 0.44, 0.10, -17.90, 13.49, -0.08, -0.01, 0.18,
23314 0.20, -0.01, 0.01,-628.24, 684.99, -0.64, -0.50, 15.32,
23315 14.05, 3.18, -4.19, 0.19, -0.17, -0.09, -0.07,-866.48,
23316 -16.26, 0.52, -1.30, -0.36, 19.37, 0.43, -0.01, 0.26,
23317 -512.37, 695.54, -1.47, -1.40, 15.55, 11.46, -0.16, 0.03,
23318 0.15, -0.17, 0.01, 0.01, 506.65, 643.75, 2.54, -2.62,
23319 14.40, -11.33, -0.77, -0.06, -0.15, -0.16, 0.00, 0.01,
23320 664.57, 16.81, -0.40, 1.00, 0.38, -14.86, -3.71, -0.09,
23321 -0.20, 405.91, 522.11, 0.99, -1.50, 11.67, -9.08, -0.25,
23322 -0.02, -0.12, -0.13,-305.78, 326.60, 1.75, 1.90, 7.30,
23323 6.84, 0.20, -0.04, 300.99,-325.03, -0.44, -0.50, -7.27,
23324 -6.73, -1.01, 0.01, 0.00, 0.08, 0.00, 0.02, 438.51,
23325 10.47, -0.56, -0.20, 0.24, -9.81, -0.24, 0.01, -0.13,
23326 -264.02, 335.24, 0.99, 1.40, 7.49, 5.90, -0.27, -0.02,
23327 284.09, 307.03, 0.32, -0.40, 6.87, -6.35, -0.99, -0.01,
23328 -250.54, 327.11, 0.08, 0.40, 7.31, 5.60, -0.30, 230.72,
23329
23330 /* 468-595 */
23331 -304.46, 0.08, -0.10, -6.81, -5.16, 0.27, 229.78, 304.17,
23332 -0.60, 0.50, 6.80, -5.14, 0.33, 0.01, 256.30,-276.81,
23333 -0.28, -0.40, -6.19, -5.73, -0.14, 0.01,-212.82, 269.45,
23334 0.84, 1.20, 6.02, 4.76, 0.14, -0.02, 196.64, 272.05,
23335 -0.84, 0.90, 6.08, -4.40, 0.35, 0.02, 188.95, 272.22,
23336 -0.12, 0.30, 6.09, -4.22, 0.34,-292.37, -5.10, -0.32,
23337 -0.40, -0.11, 6.54, 0.14, 0.01, 161.79,-220.67, 0.24,
23338 0.10, -4.93, -3.62, -0.08, 261.54, -19.94, -0.95, 0.20,
23339 -0.45, -5.85, -0.13, 0.02, 142.16,-190.79, 0.20, 0.10,
23340 -4.27, -3.18, -0.07, 187.95, -4.11, -0.24, 0.30, -0.09,
23341 -4.20, -0.09, 0.01, 0.00, 0.00, -79.08, 167.90, 0.04,
23342 0.00, 3.75, 1.77, 121.98, 131.04, -0.08, 0.10, 2.93,
23343 -2.73, -0.06,-172.95, -8.11, -0.40, -0.20, -0.18, 3.87,
23344 0.09, 0.01,-160.15, -55.30, -14.04, 13.90, -1.23, 3.58,
23345 0.40, 0.31,-115.40, 123.20, 0.60, 0.70, 2.75, 2.58,
23346 0.08, -0.01,-168.26, -2.00, 0.20, -0.20, -0.04, 3.76,
23347
23348 /* 596-723 */
23349 0.08,-114.49, 123.20, 0.32, 0.40, 2.75, 2.56, 0.07,
23350 -0.01, 112.14, 120.70, 0.28, -0.30, 2.70, -2.51, -0.07,
23351 -0.01, 161.34, 4.03, 0.20, 0.20, 0.09, -3.61, -0.08,
23352 91.31, 126.64, -0.40, 0.40, 2.83, -2.04, -0.04, 0.01,
23353 105.29, 112.90, 0.44, -0.50, 2.52, -2.35, -0.07, -0.01,
23354 98.69,-106.20, -0.28, -0.30, -2.37, -2.21, -0.06, 0.01,
23355 86.74,-112.94, -0.08, -0.20, -2.53, -1.94, -0.05,-134.81,
23356 3.51, 0.20, -0.20, 0.08, 3.01, 0.07, 79.03, 107.31,
23357 -0.24, 0.20, 2.40, -1.77, -0.04, 0.01, 132.81, -10.77,
23358 -0.52, 0.10, -0.24, -2.97, -0.07, 0.01,-130.31, -0.90,
23359 0.04, 0.00, 0.00, 2.91, -78.56, 85.32, 0.00, 0.00,
23360 1.91, 1.76, 0.04, 0.00, 0.00, -41.53, 89.10, 0.02,
23361 0.00, 1.99, 0.93, 66.03, -71.00, -0.20, -0.20, -1.59,
23362 -1.48, -0.04, 60.50, 64.70, 0.36, -0.40, 1.45, -1.35,
23363 -0.04, -0.01, -52.27, -70.01, 0.00, 0.00, -1.57, 1.17,
23364 0.03, -52.95, 66.29, 0.32, 0.40, 1.48, 1.18, 0.04,
23365
23366 /* 724-851 */
23367 -0.01, 51.02, 67.25, 0.00, 0.00, 1.50, -1.14, -0.03,
23368 -55.66, -60.92, 0.16, -0.20, -1.36, 1.24, 0.03, -54.81,
23369 -59.20, -0.08, 0.20, -1.32, 1.23, 0.03, 51.32, -55.60,
23370 0.00, 0.00, -1.24, -1.15, -0.03, 48.29, 51.80, 0.20,
23371 -0.20, 1.16, -1.08, -0.03, -45.59, -49.00, -0.12, 0.10,
23372 -1.10, 1.02, 0.03, 40.54, -52.69, -0.04, -0.10, -1.18,
23373 -0.91, -0.02, -40.58, -49.51, -1.00, 1.00, -1.11, 0.91,
23374 0.04, 0.02, -43.76, 46.50, 0.36, 0.40, 1.04, 0.98,
23375 0.03, -0.01, 62.65, -5.00, -0.24, 0.00, -0.11, -1.40,
23376 -0.03, 0.01, -38.57, 49.59, 0.08, 0.10, 1.11, 0.86,
23377 0.02, -33.22, -44.04, 0.08, -0.10, -0.98, 0.74, 0.02,
23378 37.15, -39.90, -0.12, -0.10, -0.89, -0.83, -0.02, 36.68,
23379 -39.50, -0.04, -0.10, -0.88, -0.82, -0.02, -53.22, -3.91,
23380 -0.20, 0.00, -0.09, 1.19, 0.03, 32.43, -42.19, -0.04,
23381 -0.10, -0.94, -0.73, -0.02, -51.00, -2.30, -0.12, -0.10,
23382 0.00, 1.14, -29.53, -39.11, 0.04, 0.00, -0.87, 0.66,
23383
23384 /* 852-979 */
23385 0.02, 28.50, -38.92, -0.08, -0.10, -0.87, -0.64, -0.02,
23386 26.54, 36.95, -0.12, 0.10, 0.83, -0.59, -0.01, 26.54,
23387 34.59, 0.04, -0.10, 0.77, -0.59, -0.02, 28.35, -32.55,
23388 -0.16, 0.20, -0.73, -0.63, -0.01, -28.00, 30.40, 0.00,
23389 0.00, 0.68, 0.63, 0.01, -27.61, 29.40, 0.20, 0.20,
23390 0.66, 0.62, 0.02, 40.33, 0.40, -0.04, 0.10, 0.00,
23391 -0.90, -23.28, 31.61, -0.08, -0.10, 0.71, 0.52, 0.01,
23392 37.75, 0.80, 0.04, 0.10, 0.00, -0.84, 23.66, 25.80,
23393 0.00, 0.00, 0.58, -0.53, -0.01, 21.01, -27.91, 0.00,
23394 0.00, -0.62, -0.47, -0.01, -34.81, 2.89, 0.04, 0.00,
23395 0.00, 0.78, -23.49, -25.31, 0.00, 0.00, -0.57, 0.53,
23396 0.01, -23.47, 25.20, 0.16, 0.20, 0.56, 0.52, 0.02,
23397 19.58, 27.50, -0.12, 0.10, 0.62, -0.44, -0.01, -22.67,
23398 -24.40, -0.08, 0.10, -0.55, 0.51, 0.01, -19.97, 25.00,
23399 0.12, 0.20, 0.56, 0.45, 0.01, 21.28, -22.80, -0.08,
23400 -0.10, -0.51, -0.48, -0.01, -30.47, 0.91, 0.04, 0.00,
23401
23402 /* 980-1107 */
23403 0.00, 0.68, 18.58, 24.00, 0.04, -0.10, 0.54, -0.42,
23404 -0.01, -18.02, 24.40, -0.04, -0.10, 0.55, 0.40, 0.01,
23405 17.74, 22.50, 0.08, -0.10, 0.50, -0.40, -0.01, -19.41,
23406 20.70, 0.08, 0.10, 0.46, 0.43, 0.01, -18.64, 20.11,
23407 0.00, 0.00, 0.45, 0.42, 0.01, -16.75, 21.60, 0.04,
23408 0.10, 0.48, 0.37, 0.01, -18.42, -20.00, 0.00, 0.00,
23409 -0.45, 0.41, 0.01, -26.77, 1.41, 0.08, 0.00, 0.00,
23410 0.60, -26.17, -0.19, 0.00, 0.00, 0.00, 0.59, -15.52,
23411 20.51, 0.00, 0.00, 0.46, 0.35, 0.01, -25.42, -1.91,
23412 -0.08, 0.00, -0.04, 0.57, 0.45, -17.42, 18.10, 0.00,
23413 0.00, 0.40, 0.39, 0.01, 16.39, -17.60, -0.08, -0.10,
23414 -0.39, -0.37, -0.01, -14.37, 18.91, 0.00, 0.00, 0.42,
23415 0.32, 0.01, 23.39, -2.40, -0.12, 0.00, 0.00, -0.52,
23416 14.32, -18.50, -0.04, -0.10, -0.41, -0.32, -0.01, 15.69,
23417 17.08, 0.00, 0.00, 0.38, -0.35, -0.01, -22.99, 0.50,
23418 0.04, 0.00, 0.00, 0.51, 0.00, 0.00, 14.47, -17.60,
23419
23420 /* 1108-1235 */
23421 -0.01, 0.00, -0.39, -0.32, -13.33, 18.40, -0.04, -0.10,
23422 0.41, 0.30, 22.47, -0.60, -0.04, 0.00, 0.00, -0.50,
23423 -12.78, -17.41, 0.04, 0.00, -0.39, 0.29, 0.01, -14.10,
23424 -15.31, 0.04, 0.00, -0.34, 0.32, 0.01, 11.98, 16.21,
23425 -0.04, 0.00, 0.36, -0.27, -0.01, 19.65, -1.90, -0.08,
23426 0.00, 0.00, -0.44, 19.61, -1.50, -0.08, 0.00, 0.00,
23427 -0.44, 13.41, -14.30, -0.04, -0.10, -0.32, -0.30, -0.01,
23428 -13.29, 14.40, 0.00, 0.00, 0.32, 0.30, 0.01, 11.14,
23429 -14.40, -0.04, 0.00, -0.32, -0.25, -0.01, 12.24, -13.38,
23430 0.04, 0.00, -0.30, -0.27, -0.01, 10.07, -13.81, 0.04,
23431 0.00, -0.31, -0.23, -0.01, 10.46, 13.10, 0.08, -0.10,
23432 0.29, -0.23, -0.01, 16.55, -1.71, -0.08, 0.00, 0.00,
23433 -0.37, 9.75, -12.80, 0.00, 0.00, -0.29, -0.22, -0.01,
23434 9.11, 12.80, 0.00, 0.00, 0.29, -0.20, 0.00, 0.00,
23435 -6.44, -13.80, 0.00, 0.00, -0.31, 0.14, -9.19, -12.00,
23436 0.00, 0.00, -0.27, 0.21, -10.30, 10.90, 0.08, 0.10,
23437
23438 /* 1236-1363 */
23439 0.24, 0.23, 0.01, 14.92, -0.80, -0.04, 0.00, 0.00,
23440 -0.33, 10.02, -10.80, 0.00, 0.00, -0.24, -0.22, -0.01,
23441 -9.75, 10.40, 0.04, 0.00, 0.23, 0.22, 0.01, 9.67,
23442 -10.40, -0.04, 0.00, -0.23, -0.22, -0.01, -8.28, -11.20,
23443 0.04, 0.00, -0.25, 0.19, 13.32, -1.41, -0.08, 0.00,
23444 0.00, -0.30, 8.27, 10.50, 0.04, 0.00, 0.23, -0.19,
23445 0.00, 0.00, 13.13, 0.00, 0.00, 0.00, 0.00, -0.29,
23446 -12.93, 0.70, 0.04, 0.00, 0.00, 0.29, 7.91, -10.20,
23447 0.00, 0.00, -0.23, -0.18, -7.84, -10.00, -0.04, 0.00,
23448 -0.22, 0.18, 7.44, 9.60, 0.00, 0.00, 0.21, -0.17,
23449 -7.64, 9.40, 0.08, 0.10, 0.21, 0.17, 0.01, -11.38,
23450 0.60, 0.04, 0.00, 0.00, 0.25, -7.48, 8.30, 0.00,
23451 0.00, 0.19, 0.17, -10.98, -0.20, 0.00, 0.00, 0.00,
23452 0.25, 10.98, 0.20, 0.00, 0.00, 0.00, -0.25, 7.40,
23453 -7.90, -0.04, 0.00, -0.18, -0.17, -6.09, 8.40, -0.04,
23454 0.00, 0.19, 0.14, -6.94, -7.49, 0.00, 0.00, -0.17,
23455
23456 /* 1364-1491 */
23457 0.16, 6.92, 7.50, 0.04, 0.00, 0.17, -0.15, 6.20,
23458 8.09, 0.00, 0.00, 0.18, -0.14, -6.12, 7.80, 0.04,
23459 0.00, 0.17, 0.14, 5.85, -7.50, 0.00, 0.00, -0.17,
23460 -0.13, -6.48, 6.90, 0.08, 0.10, 0.15, 0.14, 0.01,
23461 6.32, 6.90, 0.00, 0.00, 0.15, -0.14, 5.61, -7.20,
23462 0.00, 0.00, -0.16, -0.13, 9.07, 0.00, 0.00, 0.00,
23463 0.00, -0.20, 5.25, 6.90, 0.00, 0.00, 0.15, -0.12,
23464 -8.47, -0.40, 0.00, 0.00, 0.00, 0.19, 6.32, -5.39,
23465 -1.11, 1.10, -0.12, -0.14, 0.02, 0.02, 5.73, -6.10,
23466 -0.04, 0.00, -0.14, -0.13, 4.70, 6.60, -0.04, 0.00,
23467 0.15, -0.11, -4.90, -6.40, 0.00, 0.00, -0.14, 0.11,
23468 -5.33, 5.60, 0.04, 0.10, 0.13, 0.12, 0.01, -4.81,
23469 6.00, 0.04, 0.00, 0.13, 0.11, 5.13, 5.50, 0.04,
23470 0.00, 0.12, -0.11, 4.50, 5.90, 0.00, 0.00, 0.13,
23471 -0.10, -4.22, 6.10, 0.00, 0.00, 0.14, -4.53, 5.70,
23472 0.00, 0.00, 0.13, 0.10, 4.18, 5.70, 0.00, 0.00,
23473
23474 /* 1492-1619 */
23475 0.13, -4.75, -5.19, 0.00, 0.00, -0.12, 0.11, -4.06,
23476 5.60, 0.00, 0.00, 0.13, -3.98, 5.60, -0.04, 0.00,
23477 0.13, 4.02, -5.40, 0.00, 0.00, -0.12, 4.49, -4.90,
23478 -0.04, 0.00, -0.11, -0.10, -3.62, -5.40, -0.16, 0.20,
23479 -0.12, 0.00, 0.01, 4.38, 4.80, 0.00, 0.00, 0.11,
23480 -6.40, -0.10, 0.00, 0.00, 0.00, 0.14, -3.98, 5.00,
23481 0.04, 0.00, 0.11, -3.82, -5.00, 0.00, 0.00, -0.11,
23482 -3.71, 5.07, 0.00, 0.00, 0.11, 4.14, 4.40, 0.00,
23483 0.00, 0.10, -6.01, -0.50, -0.04, 0.00, 0.00, 0.13,
23484 -4.04, 4.39, 0.00, 0.00, 0.10, 3.45, -4.72, 0.00,
23485 0.00, -0.11, 3.31, 4.71, 0.00, 0.00, 0.11, 3.26,
23486 -4.50, 0.00, 0.00, -0.10, -3.26, -4.50, 0.00, 0.00,
23487 -0.10, -3.34, -4.40, 0.00, 0.00, -0.10, -3.74, -4.00,
23488 3.70, 4.00, 3.34, -4.30, 3.30, -4.30, -3.66, 3.90,
23489 0.04, 3.66, 3.90, 0.04, -3.62, -3.90, -3.61, 3.90,
23490 -0.20, 5.30, 0.00, 0.00, 0.12, 3.06, 4.30, 3.30,
23491
23492 /* 1620-1747 */
23493 4.00, 0.40, 0.20, 3.10, 4.10, -3.06, 3.90, -3.30,
23494 -3.60, -3.30, 3.36, 0.01, 3.14, 3.40, -4.57, -0.20,
23495 0.00, 0.00, 0.00, 0.10, -2.70, -3.60, 2.94, -3.20,
23496 -2.90, 3.20, 2.47, -3.40, 2.55, -3.30, 2.80, -3.08,
23497 2.51, 3.30, -4.10, 0.30, -0.12, -0.10, 4.10, 0.20,
23498 -2.74, 3.00, 2.46, 3.23, -3.66, 1.20, -0.20, 0.20,
23499 3.74, -0.40, -2.51, -2.80, -3.74, 2.27, -2.90, 0.00,
23500 0.00, -2.50, 2.70, -2.51, 2.60, -3.50, 0.20, 3.38,
23501 -2.22, -2.50, 3.26, -0.40, 1.95, -2.60, 3.22, -0.40,
23502 -0.04, -1.79, -2.60, 1.91, 2.50, 0.74, 3.05, -0.04,
23503 0.08, 2.11, -2.30, -2.11, 2.20, -1.87, -2.40, 2.03,
23504 -2.20, -2.03, 2.20, 2.98, 0.00, 0.00, 2.98, -1.71,
23505 2.40, 2.94, -0.10, -0.12, 0.10, 1.67, 2.40, -1.79,
23506 2.30, -1.79, 2.20, -1.67, 2.20, 1.79, -2.00, 1.87,
23507 -1.90, 1.63, -2.10, -1.59, 2.10, 1.55, -2.10, -1.55,
23508 2.10, -2.59, -0.20, -1.75, -1.90, -1.75, 1.90, -1.83,
23509
23510 /* 1748-1875 */
23511 -1.80, 1.51, 2.00, -1.51, -2.00, 1.71, 1.80, 1.31,
23512 2.10, -1.43, 2.00, 1.43, 2.00, -2.43, -1.51, 1.90,
23513 -1.47, 1.90, 2.39, 0.20, -2.39, 1.39, 1.90, 1.39,
23514 -1.80, 1.47, -1.60, 1.47, -1.60, 1.43, -1.50, -1.31,
23515 1.60, 1.27, -1.60, -1.27, 1.60, 1.27, -1.60, 2.03,
23516 1.35, 1.50, -1.39, -1.40, 1.95, -0.20, -1.27, 1.49,
23517 1.19, 1.50, 1.27, 1.40, 1.15, 1.50, 1.87, -0.10,
23518 -1.12, -1.50, 1.87, -1.11, -1.50, -1.11, -1.50, 0.00,
23519 0.00, 1.19, 1.40, 1.27, -1.30, -1.27, -1.30, -1.15,
23520 1.40, -1.23, 1.30, -1.23, -1.30, 1.22, -1.29, 1.07,
23521 -1.40, 1.75, -0.20, -1.03, -1.40, -1.07, 1.20, -1.03,
23522 1.15, 1.07, 1.10, 1.51, -1.03, 1.10, 1.03, -1.10,
23523 0.00, 0.00, -1.03, -1.10, 0.91, -1.20, -0.88, -1.20,
23524 -0.88, 1.20, -0.95, 1.10, -0.95, -1.10, 1.43, -1.39,
23525 0.95, -1.00, -0.95, 1.00, -0.80, 1.10, 0.91, -1.00,
23526 -1.35, 0.88, 1.00, -0.83, 1.00, -0.91, 0.90, 0.91,
23527
23528 /* 1876-2003 */
23529 0.90, 0.88, -0.90, -0.76, -1.00, -0.76, 1.00, 0.76,
23530 1.00, -0.72, 1.00, 0.84, -0.90, 0.84, 0.90, 1.23,
23531 0.00, 0.00, -0.52, -1.10, -0.68, 1.00, 1.19, -0.20,
23532 1.19, 0.76, 0.90, 1.15, -0.10, 1.15, -0.10, 0.72,
23533 -0.90, -1.15, -1.15, 0.68, 0.90, -0.68, 0.90, -1.11,
23534 0.00, 0.00, 0.20, 0.79, 0.80, -1.11, -0.10, 0.00,
23535 0.00, -0.48, -1.00, -0.76, -0.80, -0.72, -0.80, -1.07,
23536 -0.10, 0.64, 0.80, -0.64, -0.80, 0.64, 0.80, 0.40,
23537 0.60, 0.52, -0.50, -0.60, -0.80, -0.71, 0.70, -0.99,
23538 0.99, 0.56, 0.80, -0.56, 0.80, 0.68, -0.70, 0.68,
23539 0.70, -0.95, -0.64, 0.70, 0.64, 0.70, -0.60, 0.70,
23540 -0.60, -0.70, -0.91, -0.10, -0.51, 0.76, -0.91, -0.56,
23541 0.70, 0.88, 0.88, -0.63, -0.60, 0.55, -0.60, -0.80,
23542 0.80, -0.80, -0.52, 0.60, 0.52, 0.60, 0.52, -0.60,
23543 -0.48, 0.60, 0.48, 0.60, 0.48, 0.60, -0.76, 0.44,
23544 -0.60, 0.52, -0.50, -0.52, 0.50, 0.40, 0.60, -0.40,
23545
23546 /* 2004-2131 */
23547 -0.60, 0.40, -0.60, 0.72, -0.72, -0.51, -0.50, -0.48,
23548 0.50, 0.48, -0.50, -0.48, 0.50, -0.48, 0.50, 0.48,
23549 -0.50, -0.48, -0.50, -0.68, -0.68, 0.44, 0.50, -0.64,
23550 -0.10, -0.64, -0.10, -0.40, 0.50, 0.40, 0.50, 0.40,
23551 0.50, 0.00, 0.00, -0.40, -0.50, -0.36, -0.50, 0.36,
23552 -0.50, 0.60, -0.60, 0.40, -0.40, 0.40, 0.40, -0.40,
23553 0.40, -0.40, 0.40, -0.56, -0.56, 0.36, -0.40, -0.36,
23554 0.40, 0.36, -0.40, -0.36, -0.40, 0.36, 0.40, 0.36,
23555 0.40, -0.52, 0.52, 0.52, 0.32, 0.40, -0.32, 0.40,
23556 -0.32, 0.40, -0.32, 0.40, 0.32, -0.40, -0.32, -0.40,
23557 0.32, -0.40, 0.28, -0.40, -0.28, 0.40, 0.28, -0.40,
23558 0.28, 0.40, 0.48, -0.48, 0.48, 0.36, -0.30, -0.36,
23559 -0.30, 0.00, 0.00, 0.20, 0.40, -0.44, 0.44, -0.44,
23560 -0.44, -0.44, -0.44, 0.32, -0.30, 0.32, 0.30, 0.24,
23561 0.30, -0.12, -0.10, -0.28, 0.30, 0.28, 0.30, 0.28,
23562 0.30, 0.28, -0.30, 0.28, -0.30, 0.28, -0.30, 0.28,
23563
23564 /* 2132-2259 */
23565 0.30, -0.28, 0.30, 0.40, 0.40, -0.24, 0.30, 0.24,
23566 -0.30, 0.24, -0.30, -0.24, -0.30, 0.24, 0.30, 0.24,
23567 -0.30, -0.24, 0.30, 0.24, -0.30, -0.24, -0.30, 0.24,
23568 -0.30, 0.24, 0.30, -0.24, 0.30, -0.24, 0.30, 0.20,
23569 -0.30, 0.20, -0.30, 0.20, -0.30, 0.20, 0.30, 0.20,
23570 -0.30, 0.20, -0.30, 0.20, 0.30, 0.20, 0.30, -0.20,
23571 -0.30, 0.20, -0.30, 0.20, -0.30, -0.36, -0.36, -0.36,
23572 -0.04, 0.30, 0.12, -0.10, -0.32, -0.24, 0.20, 0.24,
23573 0.20, 0.20, -0.20, -0.20, -0.20, -0.20, -0.20, 0.20,
23574 0.20, 0.20, -0.20, 0.20, 0.20, 0.20, 0.20, -0.20,
23575 -0.20, 0.00, 0.00, -0.20, -0.20, -0.20, 0.20, -0.20,
23576 0.20, 0.20, -0.20, -0.20, -0.20, 0.20, 0.20, 0.20,
23577 0.20, 0.20, -0.20, 0.20, -0.20, 0.28, 0.28, 0.28,
23578 0.28, 0.28, 0.28, -0.28, 0.28, 0.12, 0.00, 0.24,
23579 0.16, -0.20, 0.16, -0.20, 0.16, -0.20, 0.16, 0.20,
23580 -0.16, 0.20, 0.16, 0.20, -0.16, 0.20, -0.16, 0.20,
23581
23582 /* 2260-2387 */
23583 -0.16, 0.20, 0.16, -0.20, 0.16, 0.20, 0.16, -0.20,
23584 -0.16, 0.20, -0.16, -0.20, -0.16, 0.20, 0.16, 0.20,
23585 0.16, -0.20, 0.16, -0.20, 0.16, 0.20, 0.16, 0.20,
23586 0.16, 0.20, -0.16, -0.20, 0.16, 0.20, -0.16, 0.20,
23587 0.16, 0.20, -0.16, -0.20, 0.16, -0.20, 0.16, -0.20,
23588 -0.16, -0.20, 0.24, -0.24, -0.24, 0.24, 0.24, 0.12,
23589 0.20, 0.12, 0.20, -0.12, -0.20, 0.12, -0.20, 0.12,
23590 -0.20, -0.12, 0.20, -0.12, 0.20, -0.12, -0.20, 0.12,
23591 0.20, 0.12, 0.20, 0.12, -0.20, -0.12, 0.20, 0.12,
23592 -0.20, -0.12, 0.20, 0.12, 0.20, 0.00, 0.00, -0.12,
23593 0.20, -0.12, 0.20, 0.12, -0.20, -0.12, 0.20, 0.12,
23594 0.20, 0.00, -0.21, -0.20, 0.00, 0.00, 0.20, -0.20,
23595 -0.20, -0.20, 0.20, -0.16, -0.10, 0.00, 0.17, 0.16,
23596 0.16, 0.16, 0.16, -0.16, 0.16, 0.16, -0.16, 0.16,
23597 -0.16, 0.16, 0.12, 0.10, 0.12, -0.10, -0.12, 0.10,
23598 -0.12, 0.10, 0.12, -0.10, -0.12, 0.12, -0.12, 0.12,
23599
23600 /* 2388-2515 */
23601 -0.12, 0.12, -0.12, -0.12, -0.12, -0.12, -0.12, -0.12,
23602 -0.12, 0.12, 0.12, 0.12, 0.12, -0.12, -0.12, 0.12,
23603 0.12, 0.12, -0.12, 0.12, -0.12, -0.12, -0.12, 0.12,
23604 -0.12, -0.12, 0.12, 0.00, 0.11, 0.11,-122.67, 164.70,
23605 203.78, 273.50, 3.58, 2.74, 6.18, -4.56, 0.00, -0.04,
23606 0.00, -0.07, 57.44, -77.10, 95.82, 128.60, -1.77, -1.28,
23607 2.85, -2.14, 82.14, 89.50, 0.00, 0.00, 2.00, -1.84,
23608 -0.04, 47.73, -64.10, 23.79, 31.90, -1.45, -1.07, 0.69,
23609 -0.53, -46.38, 50.50, 0.00, 0.00, 1.13, 1.04, 0.02,
23610 -18.38, 0.00, 63.80, 0.00, 0.00, 0.41, 0.00, -1.43,
23611 59.07, 0.00, 0.00, 0.00, 0.00, -1.32, 57.28, 0.00,
23612 0.00, 0.00, 0.00, -1.28, -48.65, 0.00, -1.15, 0.00,
23613 0.00, 1.09, 0.00, 0.03, -18.30, 24.60, -17.30, -23.20,
23614 0.56, 0.41, -0.51, 0.39, -16.91, 26.90, 8.43, 13.30,
23615 0.60, 0.38, 0.31, -0.19, 1.23, -1.70, -19.13, -25.70,
23616 -0.03, -0.03, -0.58, 0.43, -0.72, 0.90, -17.34, -23.30,
23617
23618 /* 2516-2643 */
23619 0.03, 0.02, -0.52, 0.39, -19.49, -21.30, 0.00, 0.00,
23620 -0.48, 0.44, 0.01, 20.57, -20.10, 0.64, 0.70, -0.45,
23621 -0.46, 0.00, -0.01, 4.89, 5.90, -16.55, 19.90, 0.14,
23622 -0.11, 0.44, 0.37, 18.22, 19.80, 0.00, 0.00, 0.44,
23623 -0.41, -0.01, 4.89, -5.30, -16.51, -18.00, -0.11, -0.11,
23624 -0.41, 0.37, -17.86, 0.00, 17.10, 0.00, 0.00, 0.40,
23625 0.00, -0.38, 0.32, 0.00, 24.42, 0.00, 0.00, -0.01,
23626 0.00, -0.55, -23.79, 0.00, 0.00, 0.00, 0.00, 0.53,
23627 14.72, -16.00, -0.32, 0.00, -0.36, -0.33, -0.01, 0.01,
23628 3.34, -4.50, 11.86, 15.90, -0.11, -0.07, 0.35, -0.27,
23629 -3.26, 4.40, 11.62, 15.60, 0.09, 0.07, 0.35, -0.26,
23630 -19.53, 0.00, 5.09, 0.00, 0.00, 0.44, 0.00, -0.11,
23631 -13.48, 14.70, 0.00, 0.00, 0.33, 0.30, 0.01, 10.86,
23632 -14.60, 3.18, 4.30, -0.33, -0.24, 0.09, -0.07, -11.30,
23633 -15.10, 0.00, 0.00, -0.34, 0.25, 0.01, 2.03, -2.70,
23634 10.82, 14.50, -0.07, -0.05, 0.32, -0.24, 17.46, 0.00,
23635
23636 /* 2644-2771 */
23637 0.00, 0.00, 0.00, -0.39, 16.43, 0.00, 0.52, 0.00,
23638 0.00, -0.37, 0.00, -0.01, 9.35, 0.00, 13.29, 0.00,
23639 0.00, -0.21, 0.00, -0.30, -10.42, 11.40, 0.00, 0.00,
23640 0.25, 0.23, 0.01, 0.44, 0.50, -10.38, 11.30, 0.02,
23641 -0.01, 0.25, 0.23, -14.64, 0.00, 0.00, 0.00, 0.00,
23642 0.33, 0.56, 0.80, -8.67, 11.70, 0.02, -0.01, 0.26,
23643 0.19, 13.88, 0.00, -2.47, 0.00, 0.00, -0.31, 0.00,
23644 0.06, -1.99, 2.70, 7.72, 10.30, 0.06, 0.04, 0.23,
23645 -0.17, -0.20, 0.00, 13.05, 0.00, 0.00, 0.00, 0.00,
23646 -0.29, 6.92, -9.30, 3.34, 4.50, -0.21, -0.15, 0.10,
23647 -0.07, -6.60, 0.00, 10.70, 0.00, 0.00, 0.15, 0.00,
23648 -0.24, -8.04, -8.70, 0.00, 0.00, -0.19, 0.18, -10.58,
23649 0.00, -3.10, 0.00, 0.00, 0.24, 0.00, 0.07, -7.32,
23650 8.00, -0.12, -0.10, 0.18, 0.16, 1.63, 1.70, 6.96,
23651 -7.60, 0.03, -0.04, -0.17, -0.16, -3.62, 0.00, 9.86,
23652 0.00, 0.00, 0.08, 0.00, -0.22, 0.20, -0.20, -6.88,
23653
23654 /* 2772-2899 */
23655 -7.50, 0.00, 0.00, -0.17, 0.15, -8.99, 0.00, 4.02,
23656 0.00, 0.00, 0.20, 0.00, -0.09, -1.07, 1.40, -5.69,
23657 -7.70, 0.03, 0.02, -0.17, 0.13, 6.48, -7.20, -0.48,
23658 -0.50, -0.16, -0.14, -0.01, 0.01, 5.57, -7.50, 1.07,
23659 1.40, -0.17, -0.12, 0.03, -0.02, 8.71, 0.00, 3.54,
23660 0.00, 0.00, -0.19, 0.00, -0.08, 0.40, 0.00, 9.27,
23661 0.00, 0.00, -0.01, 0.00, -0.21, -6.13, 6.70, -1.19,
23662 -1.30, 0.15, 0.14, -0.03, 0.03, 5.21, -5.70, -2.51,
23663 -2.60, -0.13, -0.12, -0.06, 0.06, 5.69, -6.20, -0.12,
23664 -0.10, -0.14, -0.13, -0.01, 2.03, -2.70, 4.53, 6.10,
23665 -0.06, -0.05, 0.14, -0.10, 5.01, 5.50, -2.51, 2.70,
23666 0.12, -0.11, 0.06, 0.06, -1.91, 2.60, -4.38, -5.90,
23667 0.06, 0.04, -0.13, 0.10, 4.65, -6.30, 0.00, 0.00,
23668 -0.14, -0.10, -5.29, 5.70, 0.00, 0.00, 0.13, 0.12,
23669 -2.23, -4.00, -4.65, 4.20, -0.09, 0.05, 0.10, 0.10,
23670 -4.53, 6.10, 0.00, 0.00, 0.14, 0.10, 2.47, 2.70,
23671
23672 /* 2900-3027 */
23673 -4.46, 4.90, 0.06, -0.06, 0.11, 0.10, -5.05, 5.50,
23674 0.84, 0.90, 0.12, 0.11, 0.02, -0.02, 4.97, -5.40,
23675 -1.71, 0.00, -0.12, -0.11, 0.00, 0.04, -0.99, -1.30,
23676 4.22, -5.70, -0.03, 0.02, -0.13, -0.09, 0.99, 1.40,
23677 4.22, -5.60, 0.03, -0.02, -0.13, -0.09, -4.69, -5.20,
23678 0.00, 0.00, -0.12, 0.10, -3.42, 0.00, 6.09, 0.00,
23679 0.00, 0.08, 0.00, -0.14, -4.65, -5.10, 0.00, 0.00,
23680 -0.11, 0.10, 0.00, 0.00, -4.53, -5.00, 0.00, 0.00,
23681 -0.11, 0.10, -2.43, -2.70, -3.82, 4.20, -0.06, 0.05,
23682 0.10, 0.09, 0.00, 0.00, -4.53, 4.90, 0.00, 0.00,
23683 0.11, 0.10, -4.49, -4.90, 0.00, 0.00, -0.11, 0.10,
23684 2.67, -2.90, -3.62, -3.90, -0.06, -0.06, -0.09, 0.08,
23685 3.94, -5.30, 0.00, 0.00, -0.12, -3.38, 3.70, -2.78,
23686 -3.10, 0.08, 0.08, -0.07, 0.06, 3.18, -3.50, -2.82,
23687 -3.10, -0.08, -0.07, -0.07, 0.06, -5.77, 0.00, 1.87,
23688 0.00, 0.00, 0.13, 0.00, -0.04, 3.54, -4.80, -0.64,
23689
23690 /* 3028-3155 */
23691 -0.90, -0.11, 0.00, -0.02, -3.50, -4.70, 0.68, -0.90,
23692 -0.11, 0.00, -0.02, 5.49, 0.00, 0.00, 0.00, 0.00,
23693 -0.12, 1.83, -2.50, 2.63, 3.50, -0.06, 0.00, 0.08,
23694 3.02, -4.10, 0.68, 0.90, -0.09, 0.00, 0.02, 0.00,
23695 0.00, 5.21, 0.00, 0.00, 0.00, 0.00, -0.12, -3.54,
23696 3.80, 2.70, 3.60, -1.35, 1.80, 0.08, 0.00, 0.04,
23697 -2.90, 3.90, 0.68, 0.90, 0.09, 0.00, 0.02, 0.80,
23698 -1.10, -2.78, -3.70, -0.02, 0.00, -0.08, 4.10, 0.00,
23699 -2.39, 0.00, 0.00, -0.09, 0.00, 0.05, -1.59, 2.10,
23700 2.27, 3.00, 0.05, 0.00, 0.07, -2.63, 3.50, -0.48,
23701 -0.60, -2.94, -3.20, -2.94, 3.20, 2.27, -3.00, -1.11,
23702 -1.50, -0.07, 0.00, -0.03, -0.56, -0.80, -2.35, 3.10,
23703 0.00, -0.60, -3.42, 1.90, -0.12, -0.10, 2.63, -2.90,
23704 2.51, 2.80, -0.64, 0.70, -0.48, -0.60, 2.19, -2.90,
23705 0.24, -0.30, 2.15, 2.90, 2.15, -2.90, 0.52, 0.70,
23706 2.07, -2.80, -3.10, 0.00, 1.79, 0.00, 0.00, 0.07,
23707
23708 /* 3156-3283 */
23709 0.00, -0.04, 0.88, 0.00, -3.46, 2.11, 2.80, -0.36,
23710 0.50, 3.54, -0.20, -3.50, -1.39, 1.50, -1.91, -2.10,
23711 -1.47, 2.00, 1.39, 1.90, 2.07, -2.30, 0.91, 1.00,
23712 1.99, -2.70, 3.30, 0.00, 0.60, -0.44, -0.70, -1.95,
23713 2.60, 2.15, -2.40, -0.60, -0.70, 3.30, 0.84, 0.00,
23714 -3.10, -3.10, 0.00, -0.72, -0.32, 0.40, -1.87, -2.50,
23715 1.87, -2.50, 0.32, 0.40, -0.24, 0.30, -1.87, -2.50,
23716 -0.24, -0.30, 1.87, -2.50, -2.70, 0.00, 1.55, 2.03,
23717 2.20, -2.98, -1.99, -2.20, 0.12, -0.10, -0.40, 0.50,
23718 1.59, 2.10, 0.00, 0.00, -1.79, 2.00, -1.03, 1.40,
23719 -1.15, -1.60, 0.32, 0.50, 1.39, -1.90, 2.35, -1.27,
23720 1.70, 0.60, 0.80, -0.32, -0.40, 1.35, -1.80, 0.44,
23721 0.00, 2.23, -0.84, 0.90, -1.27, -1.40, -1.47, 1.60,
23722 -0.28, -0.30, -0.28, 0.40, -1.27, -1.70, 0.28, -0.40,
23723 -1.43, -1.50, 0.00, 0.00, -1.27, -1.70, 2.11, -0.32,
23724 -0.40, -1.23, 1.60, 1.19, -1.30, -0.72, -0.80, 0.72,
23725
23726 /* 3284-3411 */
23727 -0.80, -1.15, -1.30, -1.35, -1.50, -1.19, -1.60, -0.12,
23728 0.20, 1.79, 0.00, -0.88, -0.28, 0.40, 1.11, 1.50,
23729 -1.83, 0.00, 0.56, -0.12, 0.10, -1.27, -1.40, 0.00,
23730 0.00, 1.15, 1.50, -0.12, 0.20, 1.11, 1.50, 0.36,
23731 -0.50, -1.07, -1.40, -1.11, 1.50, 1.67, 0.00, 0.80,
23732 -1.11, 0.00, 1.43, 1.23, -1.30, -0.24, -1.19, -1.30,
23733 -0.24, 0.20, -0.44, -0.90, -0.95, 1.10, 1.07, -1.40,
23734 1.15, -1.30, 1.03, -1.10, -0.56, -0.60, -0.68, 0.90,
23735 -0.76, -1.00, -0.24, -0.30, 0.95, -1.30, 0.56, 0.70,
23736 0.84, -1.10, -0.56, 0.00, -1.55, 0.91, -1.30, 0.28,
23737 0.30, 0.16, -0.20, 0.95, 1.30, 0.40, -0.50, -0.88,
23738 -1.20, 0.95, -1.10, -0.48, -0.50, 0.00, 0.00, -1.07,
23739 1.20, 0.44, -0.50, 0.95, 1.10, 0.00, 0.00, 0.92,
23740 -1.30, 0.95, 1.00, -0.52, 0.60, 1.59, 0.24, -0.40,
23741 0.91, 1.20, 0.84, -1.10, -0.44, -0.60, 0.84, 1.10,
23742 -0.44, 0.60, -0.44, 0.60, -0.84, -1.10, -0.80, 0.00,
23743
23744 /* 3412-3539 */
23745 1.35, 0.76, 0.20, -0.91, -1.00, 0.20, -0.30, -0.91,
23746 -1.20, -0.95, 1.00, -0.48, -0.50, 0.88, 1.00, 0.48,
23747 -0.50, -0.95, -1.10, 0.20, -0.20, -0.99, 1.10, -0.84,
23748 1.10, -0.24, -0.30, 0.20, -0.30, 0.84, 1.10, -1.39,
23749 0.00, -0.28, -0.16, 0.20, 0.84, 1.10, 0.00, 0.00,
23750 1.39, 0.00, 0.00, -0.95, 1.00, 1.35, -0.99, 0.00,
23751 0.88, -0.52, 0.00, -1.19, 0.20, 0.20, 0.76, -1.00,
23752 0.00, 0.00, 0.76, 1.00, 0.00, 0.00, 0.76, 1.00,
23753 -0.76, 1.00, 0.00, 0.00, 1.23, 0.76, 0.80, -0.32,
23754 0.40, -0.72, 0.80, -0.40, -0.40, 0.00, 0.00, -0.80,
23755 -0.90, -0.68, 0.90, -0.16, -0.20, -0.16, -0.20, 0.68,
23756 -0.90, -0.36, 0.50, -0.56, -0.80, 0.72, -0.90, 0.44,
23757 -0.60, -0.48, -0.70, -0.16, 0.00, -1.11, 0.32, 0.00,
23758 -1.07, 0.60, -0.80, -0.28, -0.40, -0.64, 0.00, 0.91,
23759 1.11, 0.64, -0.90, 0.76, -0.80, 0.00, 0.00, -0.76,
23760 -0.80, 1.03, 0.00, -0.36, -0.64, -0.70, 0.36, -0.40,
23761
23762 /* 3540-3667 */
23763 1.07, 0.36, -0.50, -0.52, -0.70, 0.60, 0.00, 0.88,
23764 0.95, 0.00, 0.48, 0.16, -0.20, 0.60, 0.80, 0.16,
23765 -0.20, -0.60, -0.80, 0.00, -1.00, 0.12, 0.20, 0.16,
23766 -0.20, 0.68, 0.70, 0.59, -0.80, -0.99, -0.56, -0.60,
23767 0.36, -0.40, -0.68, -0.70, -0.68, -0.70, -0.36, -0.50,
23768 -0.44, 0.60, 0.64, 0.70, -0.12, 0.10, -0.52, 0.60,
23769 0.36, 0.40, 0.00, 0.00, 0.95, -0.84, 0.00, 0.44,
23770 0.56, 0.60, 0.32, -0.30, 0.00, 0.00, 0.60, 0.70,
23771 0.00, 0.00, 0.60, 0.70, -0.12, -0.20, 0.52, -0.70,
23772 0.00, 0.00, 0.56, 0.70, -0.12, 0.10, -0.52, -0.70,
23773 0.00, 0.00, 0.88, -0.76, 0.00, -0.44, 0.00, 0.00,
23774 -0.52, -0.70, 0.52, -0.70, 0.36, -0.40, -0.44, -0.50,
23775 0.00, 0.00, 0.60, 0.60, 0.84, 0.00, 0.12, -0.24,
23776 0.00, 0.80, -0.56, 0.60, -0.32, -0.30, 0.48, -0.50,
23777 0.28, -0.30, -0.48, -0.50, 0.12, 0.20, 0.48, -0.60,
23778 0.48, 0.60, -0.12, 0.20, 0.24, 0.00, 0.76, -0.52,
23779
23780 /* 3668-3795 */
23781 -0.60, -0.52, 0.60, 0.48, -0.50, -0.24, -0.30, 0.12,
23782 -0.10, 0.48, 0.60, 0.52, -0.20, 0.36, 0.40, -0.44,
23783 0.50, -0.24, -0.30, -0.48, -0.60, -0.44, -0.60, -0.12,
23784 0.10, 0.76, 0.76, 0.20, -0.20, 0.48, 0.50, 0.40,
23785 -0.50, -0.24, -0.30, 0.44, -0.60, 0.44, -0.60, 0.36,
23786 0.00, -0.64, 0.72, 0.00, -0.12, 0.00, -0.10, -0.40,
23787 -0.60, -0.20, -0.20, -0.44, 0.50, -0.44, 0.50, 0.20,
23788 0.20, -0.44, -0.50, 0.20, -0.20, -0.20, 0.20, -0.44,
23789 -0.50, 0.64, 0.00, 0.32, -0.36, 0.50, -0.20, -0.30,
23790 0.12, -0.10, 0.48, 0.50, -0.12, 0.30, -0.36, -0.50,
23791 0.00, 0.00, 0.48, 0.50, -0.48, 0.50, 0.68, 0.00,
23792 -0.12, 0.56, -0.40, 0.44, -0.50, -0.12, -0.10, 0.24,
23793 0.30, -0.40, 0.40, 0.64, 0.00, -0.24, 0.64, 0.00,
23794 -0.20, 0.00, 0.00, 0.44, -0.50, 0.44, 0.50, -0.12,
23795 0.20, -0.36, -0.50, 0.12, 0.00, 0.64, -0.40, 0.50,
23796 0.00, 0.10, 0.00, 0.00, -0.40, 0.50, 0.00, 0.00,
23797
23798 /* 3796-3923 */
23799 -0.40, -0.50, 0.56, 0.00, 0.28, 0.00, 0.10, 0.36,
23800 0.50, 0.00, -0.10, 0.36, -0.50, 0.36, 0.50, 0.00,
23801 -0.10, 0.24, -0.20, -0.36, -0.40, 0.16, 0.20, 0.40,
23802 -0.40, 0.00, 0.00, -0.36, -0.50, -0.36, -0.50, -0.32,
23803 -0.50, -0.12, 0.10, 0.20, 0.20, -0.36, 0.40, -0.60,
23804 0.60, 0.28, 0.00, 0.52, 0.12, -0.10, 0.40, 0.40,
23805 0.00, -0.50, 0.20, -0.20, -0.32, 0.40, 0.16, 0.20,
23806 -0.16, 0.20, 0.32, 0.40, 0.56, 0.00, -0.12, 0.32,
23807 -0.40, -0.16, -0.20, 0.00, 0.00, 0.40, 0.40, -0.40,
23808 -0.40, -0.40, 0.40, -0.36, 0.40, 0.12, 0.10, 0.00,
23809 0.10, 0.36, 0.40, 0.00, -0.10, 0.36, 0.40, -0.36,
23810 0.40, 0.00, 0.10, 0.32, 0.00, 0.44, 0.12, 0.20,
23811 0.28, -0.40, 0.00, 0.00, 0.36, 0.40, 0.32, -0.40,
23812 -0.16, 0.12, 0.10, 0.32, -0.40, 0.20, 0.30, -0.24,
23813 0.30, 0.00, 0.10, 0.32, 0.40, 0.00, -0.10, -0.32,
23814 -0.40, -0.32, 0.40, 0.00, 0.10, -0.52, -0.52, 0.52,
23815
23816 /* 3924-4051 */
23817 0.32, -0.40, 0.00, 0.00, 0.32, 0.40, 0.32, -0.40,
23818 0.00, 0.00, -0.32, -0.40, -0.32, 0.40, 0.32, 0.40,
23819 0.00, 0.00, 0.32, 0.40, 0.00, 0.00, -0.32, -0.40,
23820 0.00, 0.00, 0.32, 0.40, 0.16, 0.20, 0.32, -0.30,
23821 -0.16, 0.00, -0.48, -0.20, 0.20, -0.28, -0.30, 0.28,
23822 -0.40, 0.00, 0.00, 0.28, -0.40, 0.00, 0.00, 0.28,
23823 -0.40, 0.00, 0.00, -0.28, -0.40, 0.28, 0.40, -0.28,
23824 -0.40, -0.48, -0.20, 0.20, 0.24, 0.30, 0.44, 0.00,
23825 0.16, 0.24, 0.30, 0.16, -0.20, 0.24, 0.30, -0.12,
23826 0.20, 0.20, 0.30, -0.16, 0.20, 0.00, 0.00, 0.44,
23827 -0.32, 0.30, 0.24, 0.00, -0.36, 0.36, 0.00, 0.24,
23828 0.12, -0.20, 0.20, 0.30, -0.12, 0.00, -0.28, 0.30,
23829 -0.24, 0.30, 0.12, 0.10, -0.28, -0.30, -0.28, 0.30,
23830 0.00, 0.00, -0.28, -0.30, 0.00, 0.00, -0.28, -0.30,
23831 0.00, 0.00, 0.28, 0.30, 0.00, 0.00, -0.28, -0.30,
23832 -0.28, 0.30, 0.00, 0.00, -0.28, -0.30, 0.00, 0.00,
23833
23834 /* 4052-4179 */
23835 0.28, 0.30, 0.00, 0.00, -0.28, 0.30, 0.28, -0.30,
23836 -0.28, 0.30, 0.40, 0.40, -0.24, 0.30, 0.00, -0.10,
23837 0.16, 0.00, 0.36, -0.20, 0.30, -0.12, -0.10, -0.24,
23838 -0.30, 0.00, 0.00, -0.24, 0.30, -0.24, 0.30, 0.00,
23839 0.00, -0.24, 0.30, -0.24, 0.30, 0.24, -0.30, 0.00,
23840 0.00, 0.24, -0.30, 0.00, 0.00, 0.24, 0.30, 0.24,
23841 -0.30, 0.24, 0.30, -0.24, 0.30, -0.24, 0.30, -0.20,
23842 0.20, -0.16, -0.20, 0.00, 0.00, -0.32, 0.20, 0.00,
23843 0.10, 0.20, -0.30, 0.20, -0.20, 0.12, 0.20, -0.16,
23844 0.20, 0.16, 0.20, 0.20, 0.30, 0.20, 0.30, 0.00,
23845 0.00, -0.20, 0.30, 0.00, 0.00, 0.20, 0.30, -0.20,
23846 -0.30, -0.20, -0.30, 0.20, -0.30, 0.00, 0.00, 0.20,
23847 0.30, 0.00, 0.00, 0.20, 0.30, 0.00, 0.00, 0.20,
23848 0.30, 0.00, 0.00, 0.20, 0.30, 0.00, 0.00, 0.20,
23849 -0.30, 0.00, 0.00, -0.20, -0.30, 0.00, 0.00, -0.20,
23850 0.30, 0.00, 0.00, -0.20, 0.30, 0.00, 0.00, 0.36,
23851
23852 /* 4180-4307 */
23853 0.00, 0.00, 0.36, 0.12, 0.10, -0.24, 0.20, 0.12,
23854 -0.20, -0.16, -0.20, -0.13, 0.10, 0.22, 0.21, 0.20,
23855 0.00, -0.28, 0.32, 0.00, -0.12, -0.20, -0.20, 0.12,
23856 -0.10, 0.12, 0.10, -0.20, 0.20, 0.00, 0.00, -0.32,
23857 0.32, 0.00, 0.00, 0.32, 0.32, 0.00, 0.00, -0.24,
23858 -0.20, 0.24, 0.20, 0.20, 0.00, -0.24, 0.00, 0.00,
23859 -0.24, -0.20, 0.00, 0.00, 0.24, 0.20, -0.24, -0.20,
23860 0.00, 0.00, -0.24, 0.20, 0.16, -0.20, 0.12, 0.10,
23861 0.20, 0.20, 0.00, -0.10, -0.12, 0.10, -0.16, -0.20,
23862 -0.12, -0.10, -0.16, 0.20, 0.20, 0.20, 0.00, 0.00,
23863 -0.20, 0.20, -0.20, 0.20, -0.20, 0.20, -0.20, 0.20,
23864 0.20, -0.20, -0.20, -0.20, 0.00, 0.00, -0.20, 0.20,
23865 0.20, 0.00, -0.20, 0.00, 0.00, -0.20, 0.20, -0.20,
23866 0.20, -0.20, -0.20, -0.20, -0.20, 0.00, 0.00, 0.20,
23867 0.20, 0.20, 0.20, 0.12, -0.20, -0.12, -0.10, 0.28,
23868 -0.28, 0.16, -0.20, 0.00, -0.10, 0.00, 0.10, -0.16,
23869
23870 /* 4308-4435 */
23871 0.20, 0.00, -0.10, -0.16, -0.20, 0.00, -0.10, 0.16,
23872 -0.20, 0.16, -0.20, 0.00, 0.00, 0.16, 0.20, -0.16,
23873 0.20, 0.00, 0.00, 0.16, 0.20, 0.16, -0.20, 0.16,
23874 -0.20, -0.16, 0.20, 0.16, -0.20, 0.00, 0.00, 0.16,
23875 0.20, 0.00, 0.00, 0.16, 0.20, 0.00, 0.00, -0.16,
23876 -0.20, 0.16, -0.20, -0.16, -0.20, 0.00, 0.00, -0.16,
23877 -0.20, 0.00, 0.00, -0.16, 0.20, 0.00, 0.00, 0.16,
23878 -0.20, 0.16, 0.20, 0.16, 0.20, 0.00, 0.00, -0.16,
23879 -0.20, 0.00, 0.00, -0.16, -0.20, 0.00, 0.00, 0.16,
23880 0.20, 0.16, 0.20, 0.00, 0.00, 0.16, 0.20, 0.16,
23881 -0.20, 0.16, 0.20, 0.00, 0.00, -0.16, 0.20, 0.00,
23882 0.10, 0.12, -0.20, 0.12, -0.20, 0.00, -0.10, 0.00,
23883 -0.10, 0.12, 0.20, 0.00, -0.10, -0.12, 0.20, -0.15,
23884 0.20, -0.24, 0.24, 0.00, 0.00, 0.24, 0.24, 0.12,
23885 -0.20, -0.12, -0.20, 0.00, 0.00, 0.12, 0.20, 0.12,
23886 -0.20, 0.12, 0.20, 0.12, 0.20, 0.12, 0.20, 0.12,
23887
23888 /* 4436-4563 */
23889 -0.20, -0.12, 0.20, 0.00, 0.00, 0.12, 0.20, 0.12,
23890 0.00, -0.20, 0.00, 0.00, -0.12, -0.20, 0.12, -0.20,
23891 0.00, 0.00, 0.12, 0.20, -0.12, 0.20, -0.12, 0.20,
23892 0.12, -0.20, 0.00, 0.00, 0.12, 0.20, 0.20, 0.00,
23893 0.12, 0.00, 0.00, -0.12, 0.20, 0.00, 0.00, -0.12,
23894 -0.20, 0.00, 0.00, -0.12, -0.20, -0.12, -0.20, 0.00,
23895 0.00, 0.12, -0.20, 0.12, -0.20, 0.12, 0.20, -0.12,
23896 -0.20, 0.00, 0.00, 0.12, -0.20, 0.12, -0.20, 0.12,
23897 0.20, 0.12, 0.00, 0.20, -0.12, -0.20, 0.00, 0.00,
23898 0.12, 0.20, -0.16, 0.00, 0.16, -0.20, 0.20, 0.00,
23899 0.00, -0.20, 0.00, 0.00, -0.20, 0.20, 0.00, 0.00,
23900 0.20, 0.20, -0.20, 0.00, 0.00, -0.20, 0.12, 0.00,
23901 -0.16, 0.20, 0.00, 0.00, 0.20, 0.12, -0.10, 0.00,
23902 0.10, 0.16, -0.16, -0.16, -0.16, -0.16, -0.16, 0.00,
23903 0.00, -0.16, 0.00, 0.00, -0.16, -0.16, -0.16, 0.00,
23904 0.00, -0.16, 0.00, 0.00, 0.16, 0.00, 0.00, 0.16,
23905
23906 /* 4564-4691 */
23907 0.00, 0.00, 0.16, 0.16, 0.00, 0.00, -0.16, 0.00,
23908 0.00, -0.16, -0.16, 0.00, 0.00, 0.16, 0.00, 0.00,
23909 -0.16, -0.16, 0.00, 0.00, -0.16, -0.16, 0.12, 0.10,
23910 0.12, -0.10, 0.12, 0.10, 0.00, 0.00, 0.12, 0.10,
23911 -0.12, 0.10, 0.00, 0.00, 0.12, 0.10, 0.12, -0.10,
23912 0.00, 0.00, -0.12, -0.10, 0.00, 0.00, 0.12, 0.10,
23913 0.12, 0.00, 0.00, 0.12, 0.00, 0.00, -0.12, 0.00,
23914 0.00, 0.12, 0.12, 0.12, 0.12, 0.12, 0.00, 0.00,
23915 0.12, 0.00, 0.00, 0.12, 0.12, 0.00, 0.00, 0.12,
23916 0.00, 0.00, 0.12, -0.12, -0.12, 0.12, 0.12, -0.12,
23917 -0.12, 0.00, 0.00, 0.12, -0.12, 0.12, 0.12, -0.12,
23918 -0.12, 0.00, 0.00, -0.12, -0.12, 0.00, 0.00, -0.12,
23919 0.12, 0.00, 0.00, 0.12, 0.00, 0.00, 0.12, 0.00,
23920 0.00, 0.12, -0.12, 0.00, 0.00, -0.12, 0.12, -0.12,
23921 -0.12, 0.12, 0.00, 0.00, 0.12, 0.12, 0.12, -0.12,
23922 0.00, 0.00, -0.12, -0.12, -0.12, 0.00, 0.00, -0.12,
23923
23924 /* 4692-NA */
23925 -0.12, 0.00, 0.00, 0.12, 0.12, 0.00, 0.00, -0.12,
23926 -0.12, -0.12, -0.12, 0.12, 0.00, 0.00, 0.12, -0.12,
23927 0.00, 0.00, -0.12, -0.12, 0.00, 0.00, 0.12, -0.12,
23928 -0.12, -0.12, -0.12, 0.12, 0.12, -0.12, -0.12, 0.00,
23929 0.00, -0.12, 0.00, 0.00, -0.12, 0.12, 0.00, 0.00,
23930 0.12, 0.00, 0.00, -0.12, -0.12, 0.00, 0.00, -0.12,
23931 -0.12, 0.12, 0.00, 0.00, 0.12, 0.12, 0.00, 0.00,
23932 0.12, 0.00, 0.00, 0.12, 0.12, 0.08, 0.00, 0.04
23933 };
23934
23935 /* Number of amplitude coefficients */
23936 final int NA = a.length;
23937
23938 /* Amplitude usage: X or Y, sin or cos, power of T. */
23939 final int jaxy[] = {0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1};
23940 final int jasc[] = {0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0};
23941 final int japt[] = {0,0,0,0,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4};
23942
23943 /* Miscellaneous */
23944 double t, w, pt[] = new double[MAXPT+1], fa[] = new double[14], xypr[] = new double[2], xypl[] = new double[2], xyls[] = new double[2], arg,
23945 sc[] = new double[2];
23946 int jpt, i, j, jxy, ialast, ifreq, m, ia, jsc;
23947
23948 /*--------------------------------------------------------------------*/
23949
23950 /* Interval between fundamental date J2000.0 and given date (JC). */
23951 t = ((date1 - DJ00) + date2) / DJC;
23952
23953 /* Powers of T. */
23954 w = 1.0;
23955 for (jpt = 0; jpt <= MAXPT; jpt++) {
23956 pt[jpt] = w;
23957 w *= t;
23958 }
23959
23960 /* Initialize totals in X and Y: polynomial, luni-solar, planetary. */
23961 for (jxy = 0; jxy < 2; jxy++) {
23962 xypr[jxy] = 0.0;
23963 xyls[jxy] = 0.0;
23964 xypl[jxy] = 0.0;
23965 }
23966
23967 /* --------------------------------- */
23968 /* Fundamental arguments (IERS 2003) */
23969 /* --------------------------------- */
23970
23971 /* Mean anomaly of the Moon. */
23972 fa[0] = jauFal03(t);
23973
23974 /* Mean anomaly of the Sun. */
23975 fa[1] = jauFalp03(t);
23976
23977 /* Mean argument of the latitude of the Moon. */
23978 fa[2] = jauFaf03(t);
23979
23980 /* Mean elongation of the Moon from the Sun. */
23981 fa[3] = jauFad03(t);
23982
23983 /* Mean longitude of the ascending node of the Moon. */
23984 fa[4] = jauFaom03(t);
23985
23986 /* Planetary longitudes, Mercury through Neptune. */
23987 fa[5] = jauFame03(t);
23988 fa[6] = jauFave03(t);
23989 fa[7] = jauFae03(t);
23990 fa[8] = jauFama03(t);
23991 fa[9] = jauFaju03(t);
23992 fa[10] = jauFasa03(t);
23993 fa[11] = jauFaur03(t);
23994 fa[12] = jauFane03(t);
23995
23996 /* General accumulated precession in longitude. */
23997 fa[13] = jauFapa03(t);
23998
23999 /* -------------------------------------- */
24000 /* Polynomial part of precession-nutation */
24001 /* -------------------------------------- */
24002
24003 for (jxy = 0; jxy < 2; jxy++) {
24004 for (j = MAXPT; j >= 0; j--) {
24005 xypr[jxy] += xyp[jxy][j] * pt[j];
24006 }
24007 }
24008
24009 /* ---------------------------------- */
24010 /* Nutation periodic terms, planetary */
24011 /* ---------------------------------- */
24012
24013 /* Work backwards through the coefficients per frequency list. */
24014 ialast = NA;
24015 for (ifreq = NFPL-1; ifreq >= 0; ifreq--) {
24016
24017 /* Obtain the argument functions. */
24018 arg = 0.0;
24019 for (i = 0; i < 14; i++) {
24020 m = mfapl[ifreq][i];
24021 if (m != 0) arg += (double)m * fa[i];
24022 }
24023 sc[0] = sin(arg);
24024 sc[1] = cos(arg);
24025
24026 /* Work backwards through the amplitudes at this frequency. */
24027 ia = nc[ifreq+NFLS];
24028 for (i = ialast; i >= ia; i--) {
24029
24030 /* Coefficient number (0 = 1st). */
24031 j = i-ia;
24032
24033 /* X or Y. */
24034 jxy = jaxy[j];
24035
24036 /* Sin or cos. */
24037 jsc = jasc[j];
24038
24039 /* Power of T. */
24040 jpt = japt[j];
24041
24042 /* Accumulate the component. */
24043 xypl[jxy] += a[i-1] * sc[jsc] * pt[jpt];
24044 }
24045 ialast = ia-1;
24046 }
24047
24048 /* ----------------------------------- */
24049 /* Nutation periodic terms, luni-solar */
24050 /* ----------------------------------- */
24051
24052 /* Continue working backwards through the number of coefficients list. */
24053 for (ifreq = NFLS-1; ifreq >= 0; ifreq--) {
24054
24055 /* Obtain the argument functions. */
24056 arg = 0.0;
24057 for (i = 0; i < 5; i++) {
24058 m = mfals[ifreq][i];
24059 if (m != 0) arg += (double)m * fa[i];
24060 }
24061 sc[0] = sin(arg);
24062 sc[1] = cos(arg);
24063
24064 /* Work backwards through the amplitudes at this frequency. */
24065 ia = nc[ifreq];
24066 for (i = ialast; i >= ia; i--) {
24067
24068 /* Coefficient number (0 = 1st). */
24069 j = i-ia;
24070
24071 /* X or Y. */
24072 jxy = jaxy[j];
24073
24074 /* Sin or cos. */
24075 jsc = jasc[j];
24076
24077 /* Power of T. */
24078 jpt = japt[j];
24079
24080 /* Accumulate the component. */
24081 xyls[jxy] += a[i-1] * sc[jsc] * pt[jpt];
24082 }
24083 ialast = ia-1;
24084 }
24085
24086 /* ------------------------------------ */
24087 /* Results: CIP unit vector components */
24088 /* ------------------------------------ */
24089
24090 double x = DAS2R * (xypr[0] + (xyls[0] + xypl[0]) / 1e6);
24091 double y = DAS2R * (xypr[1] + (xyls[1] + xypl[1]) / 1e6);
24092
24093 return new CelestialIntermediatePole(x, y);
24094
24095 }
24096
24097
24098 /**
24099 * For a given TT date, compute the X,Y coordinates of the Celestial
24100 * Intermediate Pole and the CIO locator s, using the IAU 2000A
24101 * precession-nutation model.
24102 *
24103 *<p>This function is derived from the International Astronomical Union's
24104 * SOFA (Standards Of Fundamental Astronomy) software collection.
24105 *
24106 *<p>Status: support function.
24107 *
24108 *<!-- Given: -->
24109 * @param date1 double TT as a 2-part Julian Date (Note 1)
24110 * @param date2 double TT as a 2-part Julian Date (Note 1)
24111 *
24112 *<!-- Returned: -->
24113 * @return x double <u>returned</u> Celestial Intermediate Pole (Note 2)
24114 * y double <u>returned</u> Celestial Intermediate Pole (Note 2)
24115 * s double <u>returned</u> the CIO locator s (Note 2)
24116 *
24117 * <p>Notes:
24118 * <ol>
24119 *
24120 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
24121 * convenient way between the two arguments. For example,
24122 * JD(TT)=2450123.7 could be expressed in any of these ways,
24123 * among others:
24124 *<pre>
24125 * date1 date2
24126 *
24127 * 2450123.7 0.0 (JD method)
24128 * 2451545.0 -1421.3 (J2000 method)
24129 * 2400000.5 50123.2 (MJD method)
24130 * 2450123.5 0.2 (date & time method)
24131 *</pre>
24132 * The JD method is the most natural and convenient to use in
24133 * cases where the loss of several decimal digits of resolution
24134 * is acceptable. The J2000 method is best matched to the way
24135 * the argument is handled internally and will deliver the
24136 * optimum resolution. The MJD method and the date & time methods
24137 * are both good compromises between resolution and convenience.
24138 *
24139 * <li> The Celestial Intermediate Pole coordinates are the x,y
24140 * components of the unit vector in the Geocentric Celestial
24141 * Reference System.
24142 *
24143 * <li> The CIO locator s (in radians) positions the Celestial
24144 * Intermediate Origin on the equator of the CIP.
24145 *
24146 * <li> A faster, but slightly less accurate result (about 1 mas for
24147 * X,Y), can be obtained by using instead the jauXys00b function.
24148 *</ol>
24149 *<p>Called:<ul>
24150 * <li>{@link #jauPnm00a} classical NPB matrix, IAU 2000A
24151 * <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
24152 * <li>{@link #jauS00} the CIO locator s, given X,Y, IAU 2000A
24153 * </ul>
24154 *<p>Reference:
24155 *
24156 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
24157 * IERS Technical Note No. 32, BKG (2004)
24158 *
24159 *@version 2008 May 12
24160 *
24161 * @since Release 20101201
24162 *
24163 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
24164 */
24165 public static ICRFrame jauXys00a(double date1, double date2)
24166 {
24167
24168 /* Form the bias-precession-nutation matrix, IAU 2000A. */
24169 double rbpn[][] = jauPnm00a(date1, date2);
24170
24171 /* Extract X,Y. */
24172 CelestialIntermediatePole cip = jauBpn2xy(rbpn);
24173
24174 /* Obtain s. */
24175 double s = jauS00(date1, date2, cip.x, cip.y);
24176
24177 return new ICRFrame(cip, s);
24178
24179 }
24180
24181
24182 /**
24183 * The Celestial Intermediate Pole coordinates are the x,y
24184 * components of the unit vector in the Geocentric Celestial
24185 * Reference System.
24186 *
24187 * The CIO locator s (in radians) positions the Celestial
24188 * Intermediate Origin on the equator of the CIP.
24189
24190 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 1 Feb 2010
24191 *
24192 * @since AIDA Stage 1
24193 */
24194 public static class ICRFrame {
24195 public CelestialIntermediatePole cip;
24196 public double s;
24197 public ICRFrame(CelestialIntermediatePole cip, double s) {
24198 this.cip = cip;
24199 this.s = s;
24200 }
24201 }
24202 /**
24203 * For a given TT date, compute the X,Y coordinates of the Celestial
24204 * Intermediate Pole and the CIO locator s, using the IAU 2000B
24205 * precession-nutation model.
24206 *
24207 *<p>This function is derived from the International Astronomical Union's
24208 * SOFA (Standards Of Fundamental Astronomy) software collection.
24209 *
24210 *<p>Status: support function.
24211 *
24212 *<!-- Given: -->
24213 * @param date1 double TT as a 2-part Julian Date (Note 1)
24214 * @param date2 double TT as a 2-part Julian Date (Note 1)
24215 *
24216 *<!-- Returned: -->
24217 * @return x double <u>returned</u> Celestial Intermediate Pole (Note 2)
24218 * y double <u>returned</u> Celestial Intermediate Pole (Note 2)
24219 * s double <u>returned</u> the CIO locator s (Note 2)
24220 *
24221 * <p>Notes:
24222 * <ol>
24223 *
24224 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
24225 * convenient way between the two arguments. For example,
24226 * JD(TT)=2450123.7 could be expressed in any of these ways,
24227 * among others:
24228 *<pre>
24229 * date1 date2
24230 *
24231 * 2450123.7 0.0 (JD method)
24232 * 2451545.0 -1421.3 (J2000 method)
24233 * 2400000.5 50123.2 (MJD method)
24234 * 2450123.5 0.2 (date & time method)
24235 *</pre>
24236 * The JD method is the most natural and convenient to use in
24237 * cases where the loss of several decimal digits of resolution
24238 * is acceptable. The J2000 method is best matched to the way
24239 * the argument is handled internally and will deliver the
24240 * optimum resolution. The MJD method and the date & time methods
24241 * are both good compromises between resolution and convenience.
24242 *
24243 * <li> The Celestial Intermediate Pole coordinates are the x,y
24244 * components of the unit vector in the Geocentric Celestial
24245 * Reference System.
24246 *
24247 * <li> The CIO locator s (in radians) positions the Celestial
24248 * Intermediate Origin on the equator of the CIP.
24249 *
24250 * <li> The present function is faster, but slightly less accurate (about
24251 * 1 mas in X,Y), than the jauXys00a function.
24252 *</ol>
24253 *<p>Called:<ul>
24254 * <li>{@link #jauPnm00b} classical NPB matrix, IAU 2000B
24255 * <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
24256 * <li>{@link #jauS00} the CIO locator s, given X,Y, IAU 2000A
24257 * </ul>
24258 *<p>Reference:
24259 *
24260 * <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
24261 * IERS Technical Note No. 32, BKG (2004)
24262 *
24263 *@version 2008 May 12
24264 *
24265 * @since Release 20101201
24266 *
24267 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
24268 */
24269 public static ICRFrame jauXys00b(double date1, double date2)
24270 {
24271 double rbpn[][] = new double[3][3];
24272
24273
24274 /* Form the bias-precession-nutation matrix, IAU 2000A. */
24275 rbpn = jauPnm00b(date1, date2);
24276
24277 /* Extract X,Y. */
24278 CelestialIntermediatePole cip = jauBpn2xy(rbpn);
24279
24280 /* Obtain s. */
24281 double s = jauS00(date1, date2, cip.x, cip.y);
24282
24283 return new ICRFrame(cip, s);
24284
24285 }
24286
24287
24288 /**
24289 * For a given TT date, compute the X,Y coordinates of the Celestial
24290 * Intermediate Pole and the CIO locator s, using the IAU 2006
24291 * precession and IAU 2000A nutation models.
24292 *
24293 *<p>This function is derived from the International Astronomical Union's
24294 * SOFA (Standards Of Fundamental Astronomy) software collection.
24295 *
24296 *<p>Status: support function.
24297 *
24298 *<!-- Given: -->
24299 * @param date1 double TT as a 2-part Julian Date (Note 1)
24300 * @param date2 double TT as a 2-part Julian Date (Note 1)
24301 *
24302 *<!-- Returned: -->
24303 * @return x double <u>returned</u> Celestial Intermediate Pole (Note 2)
24304 * y double <u>returned</u> Celestial Intermediate Pole (Note 2)
24305 * s double <u>returned</u> the CIO locator s (Note 2)
24306 *
24307 * <p>Notes:
24308 * <ol>
24309 *
24310 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
24311 * convenient way between the two arguments. For example,
24312 * JD(TT)=2450123.7 could be expressed in any of these ways,
24313 * among others:
24314 *<pre>
24315 * date1 date2
24316 *
24317 * 2450123.7 0.0 (JD method)
24318 * 2451545.0 -1421.3 (J2000 method)
24319 * 2400000.5 50123.2 (MJD method)
24320 * 2450123.5 0.2 (date & time method)
24321 *</pre>
24322 * The JD method is the most natural and convenient to use in
24323 * cases where the loss of several decimal digits of resolution
24324 * is acceptable. The J2000 method is best matched to the way
24325 * the argument is handled internally and will deliver the
24326 * optimum resolution. The MJD method and the date & time methods
24327 * are both good compromises between resolution and convenience.
24328 *
24329 * <li> The Celestial Intermediate Pole coordinates are the x,y components
24330 * of the unit vector in the Geocentric Celestial Reference System.
24331 *
24332 * <li> The CIO locator s (in radians) positions the Celestial
24333 * Intermediate Origin on the equator of the CIP.
24334 *
24335 * <li> Series-based solutions for generating X and Y are also available:
24336 * see Capitaine & Wallace (2006) and jauXy06.
24337 *</ol>
24338 *<p>Called:<ul>
24339 * <li>{@link #jauPnm06a} classical NPB matrix, IAU 2006/2000A
24340 * <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
24341 * <li>{@link #jauS06} the CIO locator s, given X,Y, IAU 2006
24342 * </ul>
24343 *<p>References:
24344 *
24345 * <p>Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
24346 *
24347 * <p>Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
24348 *
24349 *@version 2008 May 11
24350 *
24351 * @since Release 20101201
24352 *
24353 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
24354 */
24355 public static ICRFrame jauXys06a(double date1, double date2)
24356 {
24357 double rbpn[][] = new double[3][3];
24358
24359
24360 /* Form the bias-precession-nutation matrix, IAU 2000A. */
24361 rbpn = jauPnm06a(date1, date2);
24362
24363 /* Extract X,Y. */
24364 CelestialIntermediatePole cip = jauBpn2xy(rbpn);
24365
24366 /* Obtain s. */
24367 double s = jauS06(date1, date2, cip.x, cip.y);
24368
24369 return new ICRFrame(cip, s);
24370
24371 }
24372
24373
24374 /**
24375 * Zero a p-vector.
24376 *
24377 *<p>This function is derived from the International Astronomical Union's
24378 * SOFA (Standards Of Fundamental Astronomy) software collection.
24379 *
24380 *<p>Status: vector/matrix support function.
24381 *
24382 *<!-- Returned: -->
24383 * @param p double[3] <u>returned</u> p-vector
24384 *
24385 *@version 2008 May 11
24386 *
24387 * @since Release 20101201
24388 *
24389 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
24390 */
24391 public static void jauZp(double p[] )
24392 {
24393 p[0] = 0.0;
24394 p[1] = 0.0;
24395 p[2] = 0.0;
24396
24397 return;
24398
24399 }
24400
24401
24402 /**
24403 * Zero a pv-vector.
24404 *
24405 *<p>This function is derived from the International Astronomical Union's
24406 * SOFA (Standards Of Fundamental Astronomy) software collection.
24407 *
24408 *<p>Status: vector/matrix support function.
24409 *
24410 *<!-- Returned: -->
24411 * @param pv double[2][3] <u>returned</u> pv-vector
24412 *
24413 *<p>Called:<ul>
24414 * <li>{@link #jauZp} zero p-vector
24415 * </ul>
24416 *@version 2008 May 11
24417 *
24418 * @since Release 20101201
24419 *
24420 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
24421 */
24422 public static void jauZpv(double pv[][])
24423 {
24424 jauZp(pv[0]);
24425 jauZp(pv[1]);
24426
24427 return;
24428
24429 }
24430
24431
24432 /**
24433 * Initialize an r-matrix to the null matrix.
24434 *
24435 *<p>This function is derived from the International Astronomical Union's
24436 * SOFA (Standards Of Fundamental Astronomy) software collection.
24437 *
24438 *<p>Status: vector/matrix support function.
24439 *
24440 *<!-- Returned: -->
24441 * @param r double[3][3] <u>returned</u> r-matrix
24442 *
24443 *@version 2008 May 11
24444 *
24445 * @since Release 20101201
24446 *
24447 * <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
24448 */
24449 public static void jauZr(double r[][])
24450 {
24451 int i, j;
24452
24453
24454 for (i = 0; i < 3; i++) {
24455 for (j = 0; j < 3; j++) {
24456 r[i][j] = 0.0;
24457 }
24458 }
24459
24460 return;
24461
24462 }
24463
24464
24465 /**
24466 * returns the first argument modulo the second.
24467 * Utility function to retain C use of fmod.
24468 * @param d
24469 * @param d2
24470 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 27 Jan 2010
24471 * @return
24472 */
24473 private static double fmod(double d, double d2) {
24474 return d % d2;
24475 }
24476 //IMPL new 20131202 routines after here
24477
24478 /**
24479 * Star-independent astrometry parameters.
24480 *
24481 * (Vectors eb, eh, em and v are all with respect to BCRS axes.)
24482 *
24483 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 26 Mar 2014
24484 * @since 20131202
24485 */
24486 public static class Astrom {
24487
24488 /** PM time interval (SSB, Julian years) */
24489 public double pmt;
24490 /** SSB to observer (vector, au) [3]*/
24491 public double eb[] = new double[3];
24492 /** Sun to observer (unit vector)[3] */
24493 public double eh[] = new double[3];
24494 /** distance from Sun to observer (au) */
24495 public double em;
24496 /** barycentric observer velocity (vector, c)[3] */
24497 public double v[] = new double[3];
24498 /** sqrt(1-|v|^2): reciprocal of Lorenz factor */
24499 public double bm1;
24500 /** bias-precession-nutation matrix [3][3] */
24501 public double bpn[][] = new double[3][3];
24502 /** longitude + s' + dERA(DUT) (radians) */
24503 public double along;
24504 /** geodetic latitude (radians) */
24505 public double phi;
24506 /** polar motion xp wrt local meridian (radians) */
24507 public double xpl;
24508 /** polar motion yp wrt local meridian (radians) */
24509 public double ypl;
24510 /** sine of geodetic latitude */
24511 public double sphi;
24512 /** cosine of geodetic latitude */
24513 public double cphi;
24514 /** magnitude of diurnal aberration vector */
24515 public double diurab;
24516 /** "local" Earth rotation angle (radians) */
24517 public double eral;
24518 /** refraction constant A (radians) */
24519 public double refa;
24520 /** refraction constant B (radians) */
24521 public double refb;
24522
24523 /**
24524 *
24525 */
24526 public Astrom(){}
24527 } ;
24528
24529 /**
24530 * Body parameters for light deflection.
24531 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 26 Mar 2014
24532 * @since 20131202
24533 */
24534 public static class Ldbody {
24535 /** mass of the body (solar masses) */
24536 public double bm;
24537 /** deflection limiter (radians^2/2) */
24538 public double dl;
24539 /** barycentric PV of the body (au, au/day)[2][3] */
24540 public double pv[][] = new double [2][3];
24541 } ;
24542
24543
24544 /**
24545 * Apply aberration to transform natural direction into proper
24546 * direction.
24547 *
24548 *<p>This function is derived from the International Astronomical Union's
24549 * SOFA (Standards of Fundamental Astronomy) software collection.
24550 *
24551 *<p>Status: support function.
24552 *
24553 *<!-- Given: -->
24554 * @param pnat double[3] natural direction to the source (unit vector)
24555 * @param v double[3] observer barycentric velocity in units of c
24556 * @param s double distance between the Sun and the observer (au)
24557 * @param bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor
24558 *
24559 *<!-- Returned:-->
24560 * @return ppr double[3] <b>Returned</b> proper direction to source (unit vector)
24561 *
24562 *<p>Notes:
24563 * <ol>
24564 *
24565 * <li> The algorithm is based on Expr. (7.40) in the Explanatory
24566 * Supplement (Urban & Seidelmann 2013), but with the following
24567 * changes:
24568 *
24569 * <p>o Rigorous rather than approximate normalization is applied.
24570 *
24571 * <p>o The gravitational potential term from Expr. (7) in
24572 * Klioner (2003) is added, taking into account only the Sun's
24573 * contribution. This has a maximum effect of about
24574 * 0.4 microarcsecond.
24575 *
24576 * <li> In almost all cases, the maximum accuracy will be limited by the
24577 * supplied velocity. For example, if the SOFA iauEpv00 function is
24578 * used, errors of up to 5 microarcseconds could occur.
24579 *
24580 * </ol>
24581 *<p>References:
24582 * <ul>
24583 *
24584 * <li> Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
24585 * the Astronomical Almanac, 3rd ed., University Science Books
24586 * (2013).
24587 *
24588 * <li> Klioner, Sergei A., "A practical relativistic model for micro-
24589 * arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003).
24590 *
24591 * </ul>
24592 * Called:
24593 * <ul>
24594 * <li>{@link #jauPdp} scalar product of two p-vectors
24595 *
24596 * </ul>
24597 *@version 2013 October 9
24598 *
24599 *@since JSOFA release 20131202
24600 *
24601 *
24602 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
24603 */
24604 public static double[] jauAb(double pnat[], double v[], double s, double bm1
24605 )
24606 {
24607 int i;
24608 double pdv, w1, w2, r2, w, p[] = new double[3], r;
24609 double ppr[] = new double[3];
24610
24611 pdv = jauPdp(pnat, v);
24612 w1 = 1.0 + pdv/(1.0 + bm1);
24613 w2 = SRS/s;
24614 r2 = 0.0;
24615 for (i = 0; i < 3; i++) {
24616 w = pnat[i]*bm1 + w1*v[i] + w2*(v[i] - pdv*pnat[i]);
24617 p[i] = w;
24618 r2 = r2 + w*w;
24619 }
24620 r = sqrt(r2);
24621 for (i = 0; i < 3; i++) {
24622 ppr[i] = p[i]/r;
24623 }
24624 return ppr;
24625 /* Finished. */
24626
24627
24628 }
24629
24630 /**
24631 * For a geocentric observer, prepare star-independent astrometry
24632 * parameters for transformations between ICRS and GCRS coordinates.
24633 * The Earth ephemeris is supplied by the caller.
24634 *
24635 * The parameters produced by this function are required in the
24636 * parallax, light deflection and aberration parts of the astrometric
24637 * transformation chain.
24638 *
24639 *<p>This function is derived from the International Astronomical Union's
24640 * SOFA (Standards of Fundamental Astronomy) software collection.
24641 *
24642 *<p>Status: support function.
24643 *
24644 *<!-- Given: -->
24645 * @param date1 double TDB as a 2-part...
24646 * @param date2 double ...Julian Date (Note 1)
24647 * @param ebpv double[2][3] Earth barycentric pos/vel (au, au/day)
24648 * @param ehp double[3] Earth heliocentric position (au)
24649 *
24650 *<!-- Returned:-->
24651 * @param astrom jauASTROM <b>Returned</b> star-independent astrometry parameters:
24652 *
24653 *<p>Notes:
24654 * <ol>
24655 *
24656 * <li> The TDB date date1+date2 is a Julian Date, apportioned in any
24657 * convenient way between the two arguments. For example,
24658 * JD(TDB)=2450123.7 could be expressed in any of these ways, among
24659 * others:
24660 * <pre>
24661 * date1 date2
24662 *
24663 * 2450123.7 0.0 (JD method)
24664 * 2451545.0 -1421.3 (J2000 method)
24665 * 2400000.5 50123.2 (MJD method)
24666 * 2450123.5 0.2 (date & time method)
24667 * </pre>
24668 * <p>The JD method is the most natural and convenient to use in cases
24669 * where the loss of several decimal digits of resolution is
24670 * acceptable. The J2000 method is best matched to the way the
24671 * argument is handled internally and will deliver the optimum
24672 * resolution. The MJD method and the date & time methods are both
24673 * good compromises between resolution and convenience. For most
24674 * applications of this function the choice will not be at all
24675 * critical.
24676 *
24677 * <p>TT can be used instead of TDB without any significant impact on
24678 * accuracy.
24679 *
24680 * <li> All the vectors are with respect to BCRS axes.
24681 *
24682 * <li> This is one of several functions that inserts into the astrom
24683 * structure star-independent parameters needed for the chain of
24684 * astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed}.
24685 *
24686 * <p>The various functions support different classes of observer and
24687 * portions of the transformation chain:
24688 * <pre>{@literal
24689 * functions observer transformation
24690 *
24691 * iauApcg iauApcg13 geocentric ICRS <-> GCRS
24692 * iauApci iauApci13 terrestrial ICRS <-> CIRS
24693 * iauApco iauApco13 terrestrial ICRS <-> observed
24694 * iauApcs iauApcs13 space ICRS <-> GCRS
24695 * iauAper iauAper13 terrestrial update Earth rotation
24696 * iauApio iauApio13 terrestrial CIRS <-> observed
24697 * }</pre>
24698 *
24699 * <p>Those with names ending in "13" use contemporary SOFA models to
24700 * compute the various ephemerides. The others accept ephemerides
24701 * supplied by the caller.
24702 *
24703 * <p>The transformation from ICRS to GCRS covers space motion,
24704 * parallax, light deflection, and aberration. From GCRS to CIRS
24705 * comprises frame bias and precession-nutation. From CIRS to
24706 * observed takes account of Earth rotation, polar motion, diurnal
24707 * aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
24708 * transformation), and atmospheric refraction.
24709 *
24710 * <li> The context structure astrom produced by this function is used by
24711 * iauAtciq* and iauAticq*.
24712 *
24713 * </ol>
24714 * Called:
24715 * <ul>
24716 * <li>{@link #jauApcs} astrometry parameters, ICRS-GCRS, space observer
24717 *
24718 * </ul>
24719 *@version 2013 October 9
24720 *
24721 *@since JSOFA release 20131202
24722 *
24723 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
24724 */
24725 public static void jauApcg(double date1, double date2,
24726 double ebpv[][], double ehp[],
24727 Astrom astrom)
24728 {
24729 /* Geocentric observer */
24730 double pv[][] = { { 0.0, 0.0, 0.0 },
24731 { 0.0, 0.0, 0.0 } };
24732
24733
24734 /* Compute the star-independent astrometry parameters. */
24735 jauApcs(date1, date2, pv, ebpv, ehp, astrom);
24736
24737 /* Finished. */
24738
24739
24740 }
24741
24742 /**
24743 * For a geocentric observer, prepare star-independent astrometry
24744 * parameters for transformations between ICRS and GCRS coordinates.
24745 * The caller supplies the date, and SOFA models are used to predict
24746 * the Earth ephemeris.
24747 *
24748 * The parameters produced by this function are required in the
24749 * parallax, light deflection and aberration parts of the astrometric
24750 * transformation chain.
24751 *
24752 *<p>This function is derived from the International Astronomical Union's
24753 * SOFA (Standards of Fundamental Astronomy) software collection.
24754 *
24755 *<p>Status: support function.
24756 *
24757 *<!-- Given: -->
24758 * @param date1 double TDB as a 2-part...
24759 * @param date2 double ...Julian Date (Note 1)
24760 *
24761 *<!-- Returned:-->
24762 * @param astrom <b>Returned</b> star-independent astrometry parameters:
24763 *
24764 *<p>Notes:
24765 * <ol>
24766 *
24767 * <li> The TDB date date1+date2 is a Julian Date, apportioned in any
24768 * convenient way between the two arguments. For example,
24769 * JD(TDB)=2450123.7 could be expressed in any of these ways, among
24770 * others:
24771 * <pre>
24772 * date1 date2
24773 *
24774 * 2450123.7 0.0 (JD method)
24775 * 2451545.0 -1421.3 (J2000 method)
24776 * 2400000.5 50123.2 (MJD method)
24777 * 2450123.5 0.2 (date & time method)
24778 * </pre>
24779 * <p>The JD method is the most natural and convenient to use in cases
24780 * where the loss of several decimal digits of resolution is
24781 * acceptable. The J2000 method is best matched to the way the
24782 * argument is handled internally and will deliver the optimum
24783 * resolution. The MJD method and the date & time methods are both
24784 * good compromises between resolution and convenience. For most
24785 * applications of this function the choice will not be at all
24786 * critical.
24787 *
24788 * <p>TT can be used instead of TDB without any significant impact on
24789 * accuracy.
24790 *
24791 * <li> All the vectors are with respect to BCRS axes.
24792 *
24793 * <li> In cases where the caller wishes to supply his own Earth
24794 * ephemeris, the function iauApcg can be used instead of the present
24795 * function.
24796 *
24797 * <li> This is one of several functions that inserts into the astrom
24798 * structure star-independent parameters needed for the chain of
24799 * astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed}.
24800 *
24801 * <p>The various functions support different classes of observer and
24802 * portions of the transformation chain:
24803 * <pre>
24804 * {@literal
24805 * functions observer transformation
24806 *
24807 * iauApcg iauApcg13 geocentric ICRS <-> GCRS
24808 * iauApci iauApci13 terrestrial ICRS <-> CIRS
24809 * iauApco iauApco13 terrestrial ICRS <-> observed
24810 * iauApcs iauApcs13 space ICRS <-> GCRS
24811 * iauAper iauAper13 terrestrial update Earth rotation
24812 * iauApio iauApio13 terrestrial CIRS <-> observed
24813 * }
24814 * </pre>
24815 * <p>Those with names ending in "13" use contemporary SOFA models to
24816 * compute the various ephemerides. The others accept ephemerides
24817 * supplied by the caller.
24818 *
24819 * <p>The transformation from ICRS to GCRS covers space motion,
24820 * parallax, light deflection, and aberration. From GCRS to CIRS
24821 * comprises frame bias and precession-nutation. From CIRS to
24822 * observed takes account of Earth rotation, polar motion, diurnal
24823 * aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
24824 * transformation), and atmospheric refraction.
24825 *
24826 * <li> The context structure astrom produced by this function is used by
24827 * iauAtciq* and iauAticq*.
24828 *
24829 * </ol>
24830 * Called:
24831 * <ul>
24832 * <li>{@link #jauEpv00} Earth position and velocity
24833 * <li>{@link #jauApcg} astrometry parameters, ICRS-GCRS, geocenter
24834 *
24835 * </ul>
24836 *@version 2013 October 9
24837 *
24838 *@since JSOFA release 20131202
24839 *
24840 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
24841 */
24842 public static void jauApcg13(double date1, double date2, Astrom astrom)
24843 {
24844 double ehpv[][] = new double[2][3], ebpv[][] = new double[2][3];
24845
24846
24847 /* Earth barycentric & heliocentric position/velocity (au, au/d). */
24848 jauEpv00(date1, date2, ehpv, ebpv);
24849
24850 /* Compute the star-independent astrometry parameters. */
24851 jauApcg(date1, date2, ebpv, ehpv[0], astrom);
24852
24853 /* Finished. */
24854
24855
24856 }
24857
24858 /**
24859 * For a terrestrial observer, prepare star-independent astrometry
24860 * parameters for transformations between ICRS and geocentric CIRS
24861 * coordinates. The Earth ephemeris and CIP/CIO are supplied by the
24862 * caller.
24863 *
24864 * The parameters produced by this function are required in the
24865 * parallax, light deflection, aberration, and bias-precession-nutation
24866 * parts of the astrometric transformation chain.
24867 *
24868 *<p>This function is derived from the International Astronomical Union's
24869 * SOFA (Standards of Fundamental Astronomy) software collection.
24870 *
24871 *<p>Status: support function.
24872 *
24873 *<!-- Given: -->
24874 * @param date1 double TDB as a 2-part...
24875 * @param date2 double ...Julian Date (Note 1)
24876 * @param ebpv double[2][3] Earth barycentric position/velocity (au, au/day)
24877 * @param ehp double[3] Earth heliocentric position (au)
24878 * @param x double CIP X,Y (components of unit vector)
24879 * @param y double CIP X,Y (components of unit vector)
24880 * @param s double the CIO locator s (radians)
24881 *
24882 *<!-- Returned:-->
24883 * @param astrom <b>Returned</b> star-independent astrometry parameters:
24884 *
24885 *<p>Notes:
24886 * <ol>
24887 *
24888 * <li> The TDB date date1+date2 is a Julian Date, apportioned in any
24889 * convenient way between the two arguments. For example,
24890 * JD(TDB)=2450123.7 could be expressed in any of these ways, among
24891 * others:
24892 * <pre>
24893 * date1 date2
24894 *
24895 * 2450123.7 0.0 (JD method)
24896 * 2451545.0 -1421.3 (J2000 method)
24897 * 2400000.5 50123.2 (MJD method)
24898 * 2450123.5 0.2 (date & time method)
24899 * </pre>
24900 * <p>The JD method is the most natural and convenient to use in cases
24901 * where the loss of several decimal digits of resolution is
24902 * acceptable. The J2000 method is best matched to the way the
24903 * argument is handled internally and will deliver the optimum
24904 * resolution. The MJD method and the date & time methods are both
24905 * good compromises between resolution and convenience. For most
24906 * applications of this function the choice will not be at all
24907 * critical.
24908 *
24909 * <p>TT can be used instead of TDB without any significant impact on
24910 * accuracy.
24911 *
24912 * <li> All the vectors are with respect to BCRS axes.
24913 *
24914 * <li> In cases where the caller does not wish to provide the Earth
24915 * ephemeris and CIP/CIO, the function iauApci13 can be used instead
24916 * of the present function. This computes the required quantities
24917 * using other SOFA functions.
24918 *
24919 * <li> This is one of several functions that inserts into the astrom
24920 * structure star-independent parameters needed for the chain of
24921 * astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
24922 *
24923 * <p>The various functions support different classes of observer and
24924 * portions of the transformation chain:
24925 * <pre>{@literal
24926 * functions observer transformation
24927 *
24928 * iauApcg iauApcg13 geocentric ICRS <-> GCRS
24929 * iauApci iauApci13 terrestrial ICRS <-> CIRS
24930 * iauApco iauApco13 terrestrial ICRS <-> observed
24931 * iauApcs iauApcs13 space ICRS <-> GCRS
24932 * iauAper iauAper13 terrestrial update Earth rotation
24933 * iauApio iauApio13 terrestrial CIRS <-> observed
24934 * }</pre>
24935 * <p>Those with names ending in "13" use contemporary SOFA models to
24936 * compute the various ephemerides. The others accept ephemerides
24937 * supplied by the caller.
24938 *
24939 * <p>The transformation from ICRS to GCRS covers space motion,
24940 * parallax, light deflection, and aberration. From GCRS to CIRS
24941 * comprises frame bias and precession-nutation. From CIRS to
24942 * observed takes account of Earth rotation, polar motion, diurnal
24943 * aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
24944 * transformation), and atmospheric refraction.
24945 *
24946 * <li> The context structure astrom produced by this function is used by
24947 * iauAtciq* and iauAticq*.
24948 *
24949 * </ol>
24950 * Called:
24951 * <ul>
24952 * <li>{@link #jauApcg} astrometry parameters, ICRS-GCRS, geocenter
24953 * <li>{@link #jauC2ixys} celestial-to-intermediate matrix, given X,Y and s
24954 *
24955 * </ul>
24956 *@version 2013 September 25
24957 *
24958 *@since JSOFA release 20131202
24959 *
24960 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
24961 */
24962 public static void jauApci(double date1, double date2,
24963 double ebpv[][], double ehp[],
24964 double x, double y, double s,
24965 Astrom astrom)
24966 {
24967
24968 /* Star-independent astrometry parameters for geocenter. */
24969 jauApcg(date1, date2, ebpv, ehp, astrom);
24970
24971 /* CIO based BPN matrix. */
24972 astrom.bpn = jauC2ixys(x, y, s);
24973
24974 /* Finished. */
24975
24976
24977 }
24978
24979 /**
24980 * For a terrestrial observer, prepare star-independent astrometry
24981 * parameters for transformations between ICRS and geocentric CIRS
24982 * coordinates. The caller supplies the date, and SOFA models are used
24983 * to predict the Earth ephemeris and CIP/CIO.
24984 *
24985 * The parameters produced by this function are required in the
24986 * parallax, light deflection, aberration, and bias-precession-nutation
24987 * parts of the astrometric transformation chain.
24988 *
24989 *<p>This function is derived from the International Astronomical Union's
24990 * SOFA (Standards of Fundamental Astronomy) software collection.
24991 *
24992 *<p>Status: support function.
24993 *
24994 *<!-- Given: -->
24995 * @param date1 double TDB as a 2-part...
24996 * @param date2 double ...Julian Date (Note 1)
24997 *
24998 *<!-- Returned:-->
24999 * @param astrom jauASTROM <b>Returned</b> star-independent astrometry parameters:
25000 * pmt double <b>Returned</b> PM time interval (SSB, Julian years)
25001 * eb double[3] <b>Returned</b> SSB to observer (vector, au)
25002 * eh double[3] <b>Returned</b> Sun to observer (unit vector)
25003 * em double <b>Returned</b> distance from Sun to observer (au)
25004 * v double[3] <b>Returned</b> barycentric observer velocity (vector, c)
25005 * bm1 double <b>Returned</b> sqrt(1-|v|^2): reciprocal of Lorenz factor
25006 * bpn double[3][3] <b>Returned</b> bias-precession-nutation matrix
25007 * along double <b>Returned</b> unchanged
25008 * xpl double <b>Returned</b> unchanged
25009 * ypl double <b>Returned</b> unchanged
25010 * sphi double <b>Returned</b> unchanged
25011 * cphi double <b>Returned</b> unchanged
25012 * diurab double <b>Returned</b> unchanged
25013 * eral double <b>Returned</b> unchanged
25014 * refa double <b>Returned</b> unchanged
25015 * refb double <b>Returned</b> unchanged
25016 * @return double* <b>Returned</b> equation of the origins (ERA-GST)
25017 *
25018 *<p>Notes:
25019 * <ol>
25020 *
25021 * <li> The TDB date date1+date2 is a Julian Date, apportioned in any
25022 * convenient way between the two arguments. For example,
25023 * JD(TDB)=2450123.7 could be expressed in any of these ways, among
25024 * others:
25025 * <pre>
25026 * date1 date2
25027 *
25028 * 2450123.7 0.0 (JD method)
25029 * 2451545.0 -1421.3 (J2000 method)
25030 * 2400000.5 50123.2 (MJD method)
25031 * 2450123.5 0.2 (date & time method)
25032 * </pre>
25033 * <p>The JD method is the most natural and convenient to use in cases
25034 * where the loss of several decimal digits of resolution is
25035 * acceptable. The J2000 method is best matched to the way the
25036 * argument is handled internally and will deliver the optimum
25037 * resolution. The MJD method and the date & time methods are both
25038 * good compromises between resolution and convenience. For most
25039 * applications of this function the choice will not be at all
25040 * critical.
25041 *
25042 * <p>TT can be used instead of TDB without any significant impact on
25043 * accuracy.
25044 *
25045 * <li> All the vectors are with respect to BCRS axes.
25046 *
25047 * <li> In cases where the caller wishes to supply his own Earth
25048 * ephemeris and CIP/CIO, the function iauApci can be used instead
25049 * of the present function.
25050 *
25051 * <li> This is one of several functions that inserts into the astrom
25052 * structure star-independent parameters needed for the chain of
25053 * astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
25054 *
25055 * <p>The various functions support different classes of observer and
25056 * portions of the transformation chain:
25057 * <pre>{@literal
25058 * functions observer transformation
25059 *
25060 * iauApcg iauApcg13 geocentric ICRS <-> GCRS
25061 * iauApci iauApci13 terrestrial ICRS <-> CIRS
25062 * iauApco iauApco13 terrestrial ICRS <-> observed
25063 * iauApcs iauApcs13 space ICRS <-> GCRS
25064 * iauAper iauAper13 terrestrial update Earth rotation
25065 * iauApio iauApio13 terrestrial CIRS <-> observed
25066 * }</pre>
25067 * <p>Those with names ending in "13" use contemporary SOFA models to
25068 * compute the various ephemerides. The others accept ephemerides
25069 * supplied by the caller.
25070 *
25071 * <p>The transformation from ICRS to GCRS covers space motion,
25072 * parallax, light deflection, and aberration. From GCRS to CIRS
25073 * comprises frame bias and precession-nutation. From CIRS to
25074 * observed takes account of Earth rotation, polar motion, diurnal
25075 * aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
25076 * transformation), and atmospheric refraction.
25077 *
25078 * <li> The context structure astrom produced by this function is used by
25079 * iauAtciq* and iauAticq*.
25080 *
25081 * </ol>
25082 * Called:
25083 * <ul>
25084 * <li>{@link #jauEpv00} Earth position and velocity
25085 * <li>{@link #jauPnm06a} classical NPB matrix, IAU 2006/2000A
25086 * <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
25087 * <li>{@link #jauS06} the CIO locator s, given X,Y, IAU 2006
25088 * <li>{@link #jauApci} astrometry parameters, ICRS-CIRS
25089 * <li>{@link #jauEors} equation of the origins, given NPB matrix and s
25090 *
25091 * </ul>
25092 *@version 2013 October 9
25093 *
25094 *@since JSOFA release 20131202
25095 *
25096 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
25097 */
25098 public static double jauApci13(double date1, double date2,
25099 Astrom astrom)
25100 {
25101 double ehpv[][] = new double[2][3], ebpv[][] = new double[2][3], r[][], s;
25102
25103
25104 /* Earth barycentric & heliocentric position/velocity (au, au/d). */
25105 jauEpv00(date1, date2, ehpv, ebpv);
25106
25107 /* Form the equinox based BPN matrix, IAU 2006/2000A. */
25108 r = jauPnm06a(date1, date2);
25109
25110 /* Extract CIP X,Y. */
25111 CelestialIntermediatePole cip = jauBpn2xy(r);
25112
25113 /* Obtain CIO locator s. */
25114 s = jauS06(date1, date2, cip.x, cip.y);
25115
25116 /* Compute the star-independent astrometry parameters. */
25117 jauApci(date1, date2, ebpv, ehpv[0], cip.x, cip.y, s, astrom);
25118
25119 /* Equation of the origins. */
25120 return jauEors(r, s);
25121
25122 /* Finished. */
25123
25124
25125 }
25126
25127 /**
25128 * For a terrestrial observer, prepare star-independent astrometry
25129 * parameters for transformations between ICRS and observed
25130 * coordinates. The caller supplies the Earth ephemeris, the Earth
25131 * rotation information and the refraction constants as well as the
25132 * site coordinates.
25133 *
25134 *<p>This function is derived from the International Astronomical Union's
25135 * SOFA (Standards of Fundamental Astronomy) software collection.
25136 *
25137 *<p>Status: support function.
25138 *
25139 *<!-- Given: -->
25140 * @param date1 double TDB as a 2-part...
25141 * @param date2 double ...Julian Date (Note 1)
25142 * @param ebpv double[2][3] Earth barycentric PV (au, au/day, Note 2)
25143 * @param ehp double[3] Earth heliocentric P (au, Note 2)
25144 * @param x double CIP X,Y (components of unit vector)
25145 * @param y double CIP X,Y (components of unit vector)
25146 * @param s double the CIO locator s (radians)
25147 * @param theta double Earth rotation angle (radians)
25148 * @param elong double longitude (radians, east +ve, Note 3)
25149 * @param phi double latitude (geodetic, radians, Note 3)
25150 * @param hm double height above ellipsoid (m, geodetic, Note 3)
25151 * @param xp double polar motion coordinates (radians, Note 4)
25152 * @param yp double polar motion coordinates (radians, Note 4)
25153 * @param sp double the TIO locator s' (radians, Note 4)
25154 * @param refa double refraction constant A (radians, Note 5)
25155 * @param refb double refraction constant B (radians, Note 5)
25156 *
25157 *<!-- Returned:-->
25158 * @param astrom <b>Returned</b> star-independent astrometry parameters:
25159 *
25160 *<p>Notes:
25161 * <ol>
25162 *
25163 * <li> The TDB date date1+date2 is a Julian Date, apportioned in any
25164 * convenient way between the two arguments. For example,
25165 * JD(TDB)=2450123.7 could be expressed in any of these ways, among
25166 * others:
25167 * <pre>
25168 * date1 date2
25169 *
25170 * 2450123.7 0.0 (JD method)
25171 * 2451545.0 -1421.3 (J2000 method)
25172 * 2400000.5 50123.2 (MJD method)
25173 * 2450123.5 0.2 (date & time method)
25174 * </pre>
25175 * <p>The JD method is the most natural and convenient to use in cases
25176 * where the loss of several decimal digits of resolution is
25177 * acceptable. The J2000 method is best matched to the way the
25178 * argument is handled internally and will deliver the optimum
25179 * resolution. The MJD method and the date & time methods are both
25180 * good compromises between resolution and convenience. For most
25181 * applications of this function the choice will not be at all
25182 * critical.
25183 *
25184 * <p>TT can be used instead of TDB without any significant impact on
25185 * accuracy.
25186 *
25187 * <li> The vectors eb, eh, and all the astrom vectors, are with respect
25188 * to BCRS axes.
25189 *
25190 * <li> The geographical coordinates are with respect to the WGS84
25191 * reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN
25192 * CONVENTION: the longitude required by the present function is
25193 * right-handed, i.e. east-positive, in accordance with geographical
25194 * convention.
25195 *
25196 * <li> xp and yp are the coordinates (in radians) of the Celestial
25197 * Intermediate Pole with respect to the International Terrestrial
25198 * Reference System (see IERS Conventions), measured along the
25199 * meridians 0 and 90 deg west respectively. sp is the TIO locator
25200 * s', in radians, which positions the Terrestrial Intermediate
25201 * Origin on the equator. For many applications, xp, yp and
25202 * (especially) sp can be set to zero.
25203 *
25204 * <p>Internally, the polar motion is stored in a form rotated onto the
25205 * local meridian.
25206 *
25207 * <li> The refraction constants refa and refb are for use in a
25208 * dZ = A*tan(Z)+B*tan^3(Z) model, where Z is the observed
25209 * (i.e. refracted) zenith distance and dZ is the amount of
25210 * refraction.
25211 *
25212 * <li> It is advisable to take great care with units, as even unlikely
25213 * values of the input parameters are accepted and processed in
25214 * accordance with the models used.
25215 *
25216 * <li> In cases where the caller does not wish to provide the Earth
25217 * Ephemeris, the Earth rotation information and refraction
25218 * constants, the function iauApco13 can be used instead of the
25219 * present function. This starts from UTC and weather readings etc.
25220 * and computes suitable values using other SOFA functions.
25221 *
25222 * <li> This is one of several functions that inserts into the astrom
25223 * structure star-independent parameters needed for the chain of
25224 * astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
25225 *
25226 * <p>The various functions support different classes of observer and
25227 * portions of the transformation chain:
25228 * <pre>{@literal
25229 * functions observer transformation
25230 *
25231 * iauApcg iauApcg13 geocentric ICRS <-> GCRS
25232 * iauApci iauApci13 terrestrial ICRS <-> CIRS
25233 * iauApco iauApco13 terrestrial ICRS <-> observed
25234 * iauApcs iauApcs13 space ICRS <-> GCRS
25235 * iauAper iauAper13 terrestrial update Earth rotation
25236 * iauApio iauApio13 terrestrial CIRS <-> observed
25237 * }</pre>
25238 * <p>Those with names ending in "13" use contemporary SOFA models to
25239 * compute the various ephemerides. The others accept ephemerides
25240 * supplied by the caller.
25241 *
25242 * <p>The transformation from ICRS to GCRS covers space motion,
25243 * parallax, light deflection, and aberration. From GCRS to CIRS
25244 * comprises frame bias and precession-nutation. From CIRS to
25245 * observed takes account of Earth rotation, polar motion, diurnal
25246 * aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
25247 * transformation), and atmospheric refraction.
25248 *
25249 * <li> The context structure astrom produced by this function is used by
25250 * iauAtioq, iauAtoiq, iauAtciq* and iauAticq*.
25251 *
25252 * </ol>
25253 * Called:
25254 * <ul>
25255 * <li>{@link #jauAper} astrometry parameters: update ERA
25256 * <li>{@link #jauC2ixys} celestial-to-intermediate matrix, given X,Y and s
25257 * <li>{@link #jauPvtob} position/velocity of terrestrial station
25258 * <li>{@link #jauTrxpv} product of transpose of r-matrix and pv-vector
25259 * <li>{@link #jauApcs} astrometry parameters, ICRS-GCRS, space observer
25260 * <li>{@link #jauCr} copy r-matrix
25261 *
25262 * </ul>
25263 *@version 2013 October 9
25264 *
25265 *@since JSOFA release 20131202
25266 *
25267 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
25268 * @throws JSOFAInternalError
25269 * @throws JSOFAIllegalParameter
25270 */
25271 public static void jauApco(double date1, double date2,
25272 double ebpv[][], double ehp[],
25273 double x, double y, double s, double theta,
25274 double elong, double phi, double hm,
25275 double xp, double yp, double sp,
25276 double refa, double refb,
25277 Astrom astrom) throws JSOFAIllegalParameter, JSOFAInternalError
25278 {
25279 double sl, cl, r[][], pvc[][], pv[][];
25280
25281
25282 /* Longitude with adjustment for TIO locator s'. */
25283 astrom.along = elong + sp;
25284
25285 /* Polar motion, rotated onto the local meridian. */
25286 sl = sin(astrom.along);
25287 cl = cos(astrom.along);
25288 astrom.xpl = xp*cl - yp*sl;
25289 astrom.ypl = xp*sl + yp*cl;
25290
25291 /* Functions of latitude. */
25292 astrom.sphi = sin(phi);
25293 astrom.cphi = cos(phi);
25294
25295 /* Refraction constants. */
25296 astrom.refa = refa;
25297 astrom.refb = refb;
25298
25299 /* Local Earth rotation angle. */
25300 jauAper(theta, astrom);
25301
25302 /* Disable the (redundant) diurnal aberration step. */
25303 astrom.diurab = 0.0;
25304
25305 /* CIO based BPN matrix. */
25306 r = jauC2ixys(x, y, s);
25307
25308 /* Observer's geocentric position and velocity (m, m/s, CIRS). */
25309 pvc = jauPvtob(elong, phi, hm, xp, yp, sp, theta);
25310
25311 /* Rotate into GCRS. */
25312 pv = jauTrxpv(r, pvc);
25313
25314 /* ICRS <-> GCRS parameters. */
25315 jauApcs(date1, date2, pv, ebpv, ehp, astrom);
25316
25317 /* Store the CIO based BPN matrix. */
25318 jauCr(r, astrom.bpn );
25319
25320 /* Finished. */
25321
25322
25323 }
25324
25325 /**
25326 * For a terrestrial observer, prepare star-independent astrometry
25327 * parameters for transformations between ICRS and observed
25328 * coordinates. The caller supplies UTC, site coordinates, ambient air
25329 * conditions and observing wavelength, and SOFA models are used to
25330 * obtain the Earth ephemeris, CIP/CIO and refraction constants.
25331 *
25332 * The parameters produced by this function are required in the
25333 * parallax, light deflection, aberration, and bias-precession-nutation
25334 * parts of the ICRS/CIRS transformations.
25335 *
25336 *<p>This function is derived from the International Astronomical Union's
25337 * SOFA (Standards of Fundamental Astronomy) software collection.
25338 *
25339 *<p>Status: support function.
25340 *
25341 *<!-- Given: -->
25342 * @param utc1 double UTC as a 2-part...
25343 * @param utc2 double ...quasi Julian Date (Notes 1,2)
25344 * @param dut1 double UT1-UTC (seconds, Note 3)
25345 * @param elong double longitude (radians, east +ve, Note 4)
25346 * @param phi double latitude (geodetic, radians, Note 4)
25347 * @param hm double height above ellipsoid (m, geodetic, Notes 4,6)
25348 * @param xp double polar motion coordinates (radians, Note 5)
25349 * @param yp double polar motion coordinates (radians, Note 5)
25350 * @param phpa double pressure at the observer (hPa = mB, Note 6)
25351 * @param tc double ambient temperature at the observer (deg C)
25352 * @param rh double relative humidity at the observer (range 0-1)
25353 * @param wl double wavelength (micrometers, Note 7)
25354 *
25355 *<!-- Returned:-->
25356 * @param astrom <b>Returned</b> star-independent astrometry parameters:
25357 *
25358 *
25359 * @return double <b>Returned</b> equation of the origins (ERA-GST)
25360 *
25361 * @throws JSOFAInternalError
25362 * @throws JSOFAIllegalParameter
25363 * int status: <b>Returned</b> +1 = dubious year (Note 2)
25364 * 0 = <b>Returned</b> OK
25365 * -1 = <b>Returned</b> unacceptable date
25366 *
25367 *<p>Notes:
25368 * <ol>
25369 *
25370 * <li> utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
25371 * convenient way between the two arguments, for example where utc1
25372 * is the Julian Day Number and utc2 is the fraction of a day.
25373 *
25374 * <p>However, JD cannot unambiguously represent UTC during a leap
25375 * second unless special measures are taken. The convention in the
25376 * present function is that the JD day represents UTC days whether
25377 * the length is 86399, 86400 or 86401 SI seconds.
25378 *
25379 * <p>Applications should use the function iauDtf2d to convert from
25380 * calendar date and time of day into 2-part quasi Julian Date, as
25381 * it implements the leap-second-ambiguity convention just
25382 * described.
25383 *
25384 * <li> The warning status "dubious year" flags UTCs that predate the
25385 * introduction of the time scale or that are too far in the
25386 * future to be trusted. See iauDat for further details.
25387 *
25388 * <li> UT1-UTC is tabulated in IERS bulletins. It increases by exactly
25389 * one second at the end of each positive UTC leap second,
25390 * introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
25391 * practice is under review, and in the future UT1-UTC may grow
25392 * essentially without limit.
25393 *
25394 * <li> The geographical coordinates are with respect to the WGS84
25395 * reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
25396 * longitude required by the present function is east-positive
25397 * (i.e. right-handed), in accordance with geographical convention.
25398 *
25399 * <li> The polar motion xp,yp can be obtained from IERS bulletins. The
25400 * values are the coordinates (in radians) of the Celestial
25401 * Intermediate Pole with respect to the International Terrestrial
25402 * Reference System (see IERS Conventions 2003), measured along the
25403 * meridians 0 and 90 deg west respectively. For many
25404 * applications, xp and yp can be set to zero.
25405 *
25406 * <p>Internally, the polar motion is stored in a form rotated onto
25407 * the local meridian.
25408 *
25409 * <li> If hm, the height above the ellipsoid of the observing station
25410 * in meters, is not known but phpa, the pressure in hPa (=mB), is
25411 * available, an adequate estimate of hm can be obtained from the
25412 * expression
25413 *
25414 * <p>hm = -29.3 * tsl * log ( phpa / 1013.25 );
25415 *
25416 * <p>where tsl is the approximate sea-level air temperature in K
25417 * (See Astrophysical Quantities, C.W.Allen, 3rd edition, section
25418 * 52). Similarly, if the pressure phpa is not known, it can be
25419 * estimated from the height of the observing station, hm, as
25420 * follows:
25421 *
25422 * <p>phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
25423 *
25424 * <p>Note, however, that the refraction is nearly proportional to
25425 * the pressure and that an accurate phpa value is important for
25426 * precise work.
25427 *
25428 * <li> The argument wl specifies the observing wavelength in
25429 * micrometers. The transition from optical to radio is assumed to
25430 * occur at 100 micrometers (about 3000 GHz).
25431 *
25432 * <li> It is advisable to take great care with units, as even unlikely
25433 * values of the input parameters are accepted and processed in
25434 * accordance with the models used.
25435 *
25436 * <li> In cases where the caller wishes to supply his own Earth
25437 * ephemeris, Earth rotation information and refraction constants,
25438 * the function iauApco can be used instead of the present function.
25439 *
25440 * <li> This is one of several functions that inserts into the astrom
25441 * structure star-independent parameters needed for the chain of
25442 * astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
25443 *
25444 * <p>The various functions support different classes of observer and
25445 * portions of the transformation chain:
25446 * <pre>{@literal
25447 * functions observer transformation
25448 *
25449 * iauApcg iauApcg13 geocentric ICRS <-> GCRS
25450 * iauApci iauApci13 terrestrial ICRS <-> CIRS
25451 * iauApco iauApco13 terrestrial ICRS <-> observed
25452 * iauApcs iauApcs13 space ICRS <-> GCRS
25453 * iauAper iauAper13 terrestrial update Earth rotation
25454 * iauApio iauApio13 terrestrial CIRS <-> observed
25455 * }</pre>
25456 * <p>Those with names ending in "13" use contemporary SOFA models to
25457 * compute the various ephemerides. The others accept ephemerides
25458 * supplied by the caller.
25459 *
25460 * <p>The transformation from ICRS to GCRS covers space motion,
25461 * parallax, light deflection, and aberration. From GCRS to CIRS
25462 * comprises frame bias and precession-nutation. From CIRS to
25463 * observed takes account of Earth rotation, polar motion, diurnal
25464 * aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
25465 * transformation), and atmospheric refraction.
25466 *
25467 * <li> The context structure astrom produced by this function is used
25468 * by iauAtioq, iauAtoiq, iauAtciq* and iauAticq*.
25469 *
25470 * </ol>
25471 * Called:
25472 * <ul>
25473 * <li>{@link #jauUtctai} UTC to TAI
25474 * <li>{@link #jauTaitt} TAI to TT
25475 * <li>{@link #jauUtcut1} UTC to UT1
25476 * <li>{@link #jauEpv00} Earth position and velocity
25477 * <li>{@link #jauPnm06a} classical NPB matrix, IAU 2006/2000A
25478 * <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
25479 * <li>{@link #jauS06} the CIO locator s, given X,Y, IAU 2006
25480 * <li>{@link #jauEra00} Earth rotation angle, IAU 2000
25481 * <li>{@link #jauSp00} the TIO locator s', IERS 2000
25482 * <li>{@link #jauRefco} refraction constants for given ambient conditions
25483 * <li>{@link #jauApco} astrometry parameters, ICRS-observed
25484 * <li>{@link #jauEors} equation of the origins, given NPB matrix and s
25485 *
25486 * </ul>
25487 *@version 2013 December 5
25488 *
25489 *@since JSOFA release 20131202
25490 *
25491 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
25492 * @throws JSOFAInternalError
25493 * @throws JSOFAIllegalParameter
25494 */
25495 public static double jauApco13(double utc1, double utc2, double dut1,
25496 double elong, double phi, double hm, double xp, double yp,
25497 double phpa, double tc, double rh, double wl,
25498 Astrom astrom ) throws JSOFAIllegalParameter, JSOFAInternalError
25499 {
25500 double ehpv[][] = new double[2][3], ebpv[][] = new double[2][3],
25501 r[][], s, theta, sp;
25502 double eo;
25503
25504
25505 /* UTC to other time scales. */
25506 JulianDate tai = jauUtctai(utc1, utc2);
25507 JulianDate tt = jauTaitt(tai.djm0, tai.djm1);
25508 JulianDate ut1 = jauUtcut1(utc1, utc2, dut1);
25509
25510 /* Earth barycentric & heliocentric position/velocity (au, au/d). */
25511 jauEpv00(tt.djm0, tt.djm1, ehpv, ebpv);
25512
25513 /* Form the equinox based BPN matrix, IAU 2006/2000A. */
25514 r = jauPnm06a(tt.djm0, tt.djm1);
25515
25516 /* Extract CIP X,Y. */
25517 CelestialIntermediatePole cip = jauBpn2xy(r);
25518
25519 /* Obtain CIO locator s. */
25520 s = jauS06(tt.djm0, tt.djm1, cip.x, cip.y);
25521
25522 /* Earth rotation angle. */
25523 theta = jauEra00(ut1.djm0, ut1.djm1);
25524
25525 /* TIO locator s'. */
25526 sp = jauSp00(tt.djm0, tt.djm1);
25527
25528 /* Refraction constants A and B. */
25529 RefCos ref = jauRefco(phpa, tc, rh, wl);
25530
25531 /* Compute the star-independent astrometry parameters. */
25532 jauApco(tt.djm0, tt.djm1, ebpv, ehpv[0], cip.x, cip.y, s, theta,
25533 elong, phi, hm, xp, yp, sp, ref.a, ref.b, astrom);
25534
25535 /* Equation of the origins. */
25536 eo = jauEors(r, s);
25537
25538 return eo;
25539
25540 /* Finished. */
25541
25542
25543 }
25544
25545 /**
25546 * For an observer whose geocentric position and velocity are known,
25547 * prepare star-independent astrometry parameters for transformations
25548 * between ICRS and GCRS. The Earth ephemeris is supplied by the
25549 * caller.
25550 *
25551 * The parameters produced by this function are required in the space
25552 * motion, parallax, light deflection and aberration parts of the
25553 * astrometric transformation chain.
25554 *
25555 *<p>This function is derived from the International Astronomical Union's
25556 * SOFA (Standards of Fundamental Astronomy) software collection.
25557 *
25558 *<p>Status: support function.
25559 *
25560 *<!-- Given: -->
25561 * @param date1 double TDB as a 2-part...
25562 * @param date2 double ...Julian Date (Note 1)
25563 * @param pv double[2][3] observer's geocentric pos/vel (m, m/s)
25564 * @param ebpv double[2][3] Earth barycentric PV (au, au/day)
25565 * @param ehp double[3] Earth heliocentric P (au)
25566 *
25567 *<!-- Returned:-->
25568 * @param astrom <b>Returned</b> star-independent astrometry parameters:
25569
25570 *<p>Notes:
25571 * <ol>
25572 *
25573 * <li> The TDB date date1+date2 is a Julian Date, apportioned in any
25574 * convenient way between the two arguments. For example,
25575 * JD(TDB)=2450123.7 could be expressed in any of these ways, among
25576 * others:
25577 * <pre>
25578 * date1 date2
25579 *
25580 * 2450123.7 0.0 (JD method)
25581 * 2451545.0 -1421.3 (J2000 method)
25582 * 2400000.5 50123.2 (MJD method)
25583 * 2450123.5 0.2 (date & time method)
25584 * </pre>
25585 * <p>The JD method is the most natural and convenient to use in cases
25586 * where the loss of several decimal digits of resolution is
25587 * acceptable. The J2000 method is best matched to the way the
25588 * argument is handled internally and will deliver the optimum
25589 * resolution. The MJD method and the date & time methods are both
25590 * good compromises between resolution and convenience. For most
25591 * applications of this function the choice will not be at all
25592 * critical.
25593 *
25594 * <p>TT can be used instead of TDB without any significant impact on
25595 * accuracy.
25596 *
25597 * <li> All the vectors are with respect to BCRS axes.
25598 *
25599 * <li> Providing separate arguments for (i) the observer's geocentric
25600 * position and velocity and (ii) the Earth ephemeris is done for
25601 * convenience in the geocentric, terrestrial and Earth orbit cases.
25602 * For deep space applications it maybe more convenient to specify
25603 * zero geocentric position and velocity and to supply the
25604 * observer's position and velocity information directly instead of
25605 * with respect to the Earth. However, note the different units:
25606 * m and m/s for the geocentric vectors, au and au/day for the
25607 * heliocentric and barycentric vectors.
25608 *
25609 * <li> In cases where the caller does not wish to provide the Earth
25610 * ephemeris, the function iauApcs13 can be used instead of the
25611 * present function. This computes the Earth ephemeris using the
25612 * SOFA function iauEpv00.
25613 *
25614 * <li> This is one of several functions that inserts into the astrom
25615 * structure star-independent parameters needed for the chain of
25616 * astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
25617 *
25618 * <p>The various functions support different classes of observer and
25619 * portions of the transformation chain:
25620 *
25621 * <pre>{@literal
25622 * functions observer transformation
25623 *
25624 * iauApcg iauApcg13 geocentric ICRS <-> GCRS
25625 * iauApci iauApci13 terrestrial ICRS <-> CIRS
25626 * iauApco iauApco13 terrestrial ICRS <-> observed
25627 * iauApcs iauApcs13 space ICRS <-> GCRS
25628 * iauAper iauAper13 terrestrial update Earth rotation
25629 * iauApio iauApio13 terrestrial CIRS <-> observed
25630 * }</pre>
25631 * <p>Those with names ending in "13" use contemporary SOFA models to
25632 * compute the various ephemerides. The others accept ephemerides
25633 * supplied by the caller.
25634 *
25635 * <p>The transformation from ICRS to GCRS covers space motion,
25636 * parallax, light deflection, and aberration. From GCRS to CIRS
25637 * comprises frame bias and precession-nutation. From CIRS to
25638 * observed takes account of Earth rotation, polar motion, diurnal
25639 * aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
25640 * transformation), and atmospheric refraction.
25641 *
25642 * <li> The context structure astrom produced by this function is used by
25643 * iauAtciq* and iauAticq*.
25644 *
25645 * </ol>
25646 * Called:
25647 * <ul>
25648 * <li>{@link #jauCp} copy p-vector
25649 * <li>{@link #jauPm} modulus of p-vector
25650 * <li>{@link #jauPn} decompose p-vector into modulus and direction
25651 * <li>{@link #jauIr} initialize r-matrix to identity
25652 *
25653 * </ul>
25654 *@version 2013 October 9
25655 *
25656 *@since JSOFA release 20131202
25657 *
25658 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
25659 */
25660 public static void jauApcs(double date1, double date2, double pv[][],
25661 double ebpv[][], double ehp[],
25662 Astrom astrom)
25663 {
25664 /* au/d to m/s */
25665 final double AUDMS = DAU/DAYSEC;
25666
25667 /* Light time for 1 AU (day) */
25668 final double CR = AULT/DAYSEC;
25669
25670 int i;
25671 double dp, dv, pb[] = new double[3], vb[] = new double[3], ph[] = new double[3], v2, w;
25672
25673
25674 /* Time since reference epoch, years (for proper motion calculation). */
25675 astrom.pmt = ( (date1 - DJ00) + date2 ) / DJY;
25676
25677 /* Adjust Earth ephemeris to observer. */
25678 for (i = 0; i < 3; i++) {
25679 dp = pv[0][i] / DAU;
25680 dv = pv[1][i] / AUDMS;
25681 pb[i] = ebpv[0][i] + dp;
25682 vb[i] = ebpv[1][i] + dv;
25683 ph[i] = ehp[i] + dp;
25684 }
25685
25686 /* Barycentric position of observer (au). */
25687 jauCp(pb, astrom.eb);
25688
25689 /* Heliocentric direction and distance (unit vector and au). */
25690 NormalizedVector nv = jauPn(ph);
25691
25692 astrom.em = nv.r;
25693 astrom.eh = nv.u;
25694
25695 /* Barycentric vel. in units of c, and reciprocal of Lorenz factor. */
25696 v2 = 0.0;
25697 for (i = 0; i < 3; i++) {
25698 w = vb[i] * CR;
25699 astrom.v[i] = w;
25700 v2 += w*w;
25701 }
25702 astrom.bm1 = sqrt(1.0 - v2);
25703
25704 /* Reset the NPB matrix. */
25705 jauIr(astrom.bpn);
25706
25707 /* Finished. */
25708
25709
25710 }
25711
25712 /**
25713 * For an observer whose geocentric position and velocity are known,
25714 * prepare star-independent astrometry parameters for transformations
25715 * between ICRS and GCRS. The Earth ephemeris is from SOFA models.
25716 *
25717 * The parameters produced by this function are required in the space
25718 * motion, parallax, light deflection and aberration parts of the
25719 * astrometric transformation chain.
25720 *
25721 *<p>This function is derived from the International Astronomical Union's
25722 * SOFA (Standards of Fundamental Astronomy) software collection.
25723 *
25724 *<p>Status: support function.
25725 *
25726 *<!-- Given: -->
25727 * @param date1 double TDB as a 2-part...
25728 * @param date2 double ...Julian Date (Note 1)
25729 * @param pv double[2][3] observer's geocentric pos/vel (Note 3)
25730 *
25731 *<!-- Returned:-->
25732 * @param astrom <b>Returned</b> star-independent astrometry parameters:
25733 *
25734 *<p>Notes:
25735 * <ol>
25736 *
25737 * <li> The TDB date date1+date2 is a Julian Date, apportioned in any
25738 * convenient way between the two arguments. For example,
25739 * JD(TDB)=2450123.7 could be expressed in any of these ways, among
25740 * others:
25741 * <pre>
25742 * date1 date2
25743 *
25744 * 2450123.7 0.0 (JD method)
25745 * 2451545.0 -1421.3 (J2000 method)
25746 * 2400000.5 50123.2 (MJD method)
25747 * 2450123.5 0.2 (date & time method)
25748 * </pre>
25749 * <p>The JD method is the most natural and convenient to use in cases
25750 * where the loss of several decimal digits of resolution is
25751 * acceptable. The J2000 method is best matched to the way the
25752 * argument is handled internally and will deliver the optimum
25753 * resolution. The MJD method and the date & time methods are both
25754 * good compromises between resolution and convenience. For most
25755 * applications of this function the choice will not be at all
25756 * critical.
25757 *
25758 * <p>TT can be used instead of TDB without any significant impact on
25759 * accuracy.
25760 *
25761 * <li> All the vectors are with respect to BCRS axes.
25762 *
25763 * <li> The observer's position and velocity pv are geocentric but with
25764 * respect to BCRS axes, and in units of m and m/s. No assumptions
25765 * are made about proximity to the Earth, and the function can be
25766 * used for deep space applications as well as Earth orbit and
25767 * terrestrial.
25768 *
25769 * <li> In cases where the caller wishes to supply his own Earth
25770 * ephemeris, the function iauApcs can be used instead of the present
25771 * function.
25772 *
25773 * <li> This is one of several functions that inserts into the astrom
25774 * structure star-independent parameters needed for the chain of
25775 * astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
25776 *
25777 * <p>The various functions support different classes of observer and
25778 * portions of the transformation chain:
25779 * <pre>{@literal
25780 * functions observer transformation
25781 *
25782 * iauApcg iauApcg13 geocentric ICRS <-> GCRS
25783 * iauApci iauApci13 terrestrial ICRS <-> CIRS
25784 * iauApco iauApco13 terrestrial ICRS <-> observed
25785 * iauApcs iauApcs13 space ICRS <-> GCRS
25786 * iauAper iauAper13 terrestrial update Earth rotation
25787 * iauApio iauApio13 terrestrial CIRS <-> observed
25788 * }</pre>
25789 * <p>Those with names ending in "13" use contemporary SOFA models to
25790 * compute the various ephemerides. The others accept ephemerides
25791 * supplied by the caller.
25792 *
25793 * <p>The transformation from ICRS to GCRS covers space motion,
25794 * parallax, light deflection, and aberration. From GCRS to CIRS
25795 * comprises frame bias and precession-nutation. From CIRS to
25796 * observed takes account of Earth rotation, polar motion, diurnal
25797 * aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
25798 * transformation), and atmospheric refraction.
25799 *
25800 * <li> The context structure astrom produced by this function is used by
25801 * iauAtciq* and iauAticq*.
25802 *
25803 * </ol>
25804 * Called:
25805 * <ul>
25806 * <li>{@link #jauEpv00} Earth position and velocity
25807 * <li>{@link #jauApcs} astrometry parameters, ICRS-GCRS, space observer
25808 *
25809 * </ul>
25810 *@version 2013 October 9
25811 *
25812 *@since JSOFA release 20131202
25813 *
25814 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
25815 */
25816 public static void jauApcs13(double date1, double date2, double pv[][],
25817 Astrom astrom)
25818 {
25819 double ehpv[][] = new double[2][3], ebpv[][] = new double[2][3];
25820
25821
25822 /* Earth barycentric & heliocentric position/velocity (au, au/d). */
25823 jauEpv00(date1, date2, ehpv, ebpv);
25824
25825 /* Compute the star-independent astrometry parameters. */
25826 jauApcs(date1, date2, pv, ebpv, ehpv[0], astrom);
25827
25828 /* Finished. */
25829
25830
25831 }
25832
25833 /**
25834 * In the star-independent astrometry parameters, update only the
25835 * Earth rotation angle, supplied by the caller explicitly.
25836 *
25837 *<p>This function is derived from the International Astronomical Union's
25838 * SOFA (Standards of Fundamental Astronomy) software collection.
25839 *
25840 *<p>Status: support function.
25841 *
25842 *<!-- Given: -->
25843 * @param theta double Earth rotation angle (radians, Note 2)
25844 * @param astrom Astrom star-independent astrometry parameters:{@code
25845 * pmt double not used
25846 * eb double[3] not used
25847 * eh double[3] not used
25848 * em double not used
25849 * v double[3] not used
25850 * bm1 double not used
25851 * bpn double[3][3] not used
25852 * along double longitude + s' (radians)
25853 * xpl double not used
25854 * ypl double not used
25855 * sphi double not used
25856 * cphi double not used
25857 * diurab double not used
25858 * eral double not used
25859 * refa double not used
25860 * refb double not used}
25861 *
25862 *<!-- Returned:-->
25863 * astrom <b>Returned</b> star-independent astrometry parameters:
25864 *
25865 *<p>Notes:
25866 * <ol>
25867 *
25868 * <li> This function exists to enable sidereal-tracking applications to
25869 * avoid wasteful recomputation of the bulk of the astrometry
25870 * parameters: only the Earth rotation is updated.
25871 *
25872 * <li> For targets expressed as equinox based positions, such as
25873 * classical geocentric apparent (RA,Dec), the supplied theta can be
25874 * Greenwich apparent sidereal time rather than Earth rotation
25875 * angle.
25876 *
25877 * <li> The function iauAper13 can be used instead of the present
25878 * function, and starts from UT1 rather than ERA itself.
25879 *
25880 * <li> This is one of several functions that inserts into the astrom
25881 * structure star-independent parameters needed for the chain of
25882 * astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
25883 *
25884 * <p>The various functions support different classes of observer and
25885 * portions of the transformation chain:
25886 * <pre>{@literal
25887 * functions observer transformation
25888 *
25889 * iauApcg iauApcg13 geocentric ICRS <-> GCRS
25890 * iauApci iauApci13 terrestrial ICRS <-> CIRS
25891 * iauApco iauApco13 terrestrial ICRS <-> observed
25892 * iauApcs iauApcs13 space ICRS <-> GCRS
25893 * iauAper iauAper13 terrestrial update Earth rotation
25894 * iauApio iauApio13 terrestrial CIRS <-> observed
25895 * }</pre>
25896 * <p>Those with names ending in "13" use contemporary SOFA models to
25897 * compute the various ephemerides. The others accept ephemerides
25898 * supplied by the caller.
25899 *
25900 * <p>The transformation from ICRS to GCRS covers space motion,
25901 * parallax, light deflection, and aberration. From GCRS to CIRS
25902 * comprises frame bias and precession-nutation. From CIRS to
25903 * observed takes account of Earth rotation, polar motion, diurnal
25904 * aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
25905 * transformation), and atmospheric refraction.
25906 *
25907 * </ol>
25908 *@version 2013 September 25
25909 *
25910 *@since JSOFA release 20131202
25911 *
25912 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
25913 */
25914 public static void jauAper(double theta, Astrom astrom)
25915 {
25916 astrom.eral = theta + astrom.along;
25917
25918 /* Finished. */
25919
25920
25921 }
25922
25923 /**
25924 * In the star-independent astrometry parameters, update only the
25925 * Earth rotation angle. The caller provides UT1, (n.b. not UTC).
25926 *
25927 *<p>This function is derived from the International Astronomical Union's
25928 * SOFA (Standards of Fundamental Astronomy) software collection.
25929 *
25930 *<p>Status: support function.
25931 *
25932 *<!-- Given: -->
25933 * @param ut11 double UT1 as a 2-part...
25934 * @param ut12 double ...Julian Date (Note 1)
25935 * @param astrom star-independent astrometry parameters:
25936 * pmt double not used
25937 * eb double[3] not used
25938 * eh double[3] not used
25939 * em double not used
25940 * v double[3] not used
25941 * bm1 double not used
25942 * bpn double[3][3] not used
25943 * along double longitude + s' (radians)
25944 * xpl double not used
25945 * ypl double not used
25946 * sphi double not used
25947 * cphi double not used
25948 * diurab double not used
25949 * eral double not used
25950 * refa double not used
25951 * refb double not used
25952 *
25953 *<!-- Returned:-->
25954 * @param astrom <b>Returned</b> star-independent astrometry parameters:
25955 *
25956 *<p>Notes:
25957 * <ol>
25958 *
25959 * <li> The UT1 date (n.b. not UTC) ut11+ut12 is a Julian Date,
25960 * apportioned in any convenient way between the arguments ut11 and
25961 * ut12. For example, JD(UT1)=2450123.7 could be expressed in any
25962 * of these ways, among others:
25963 *
25964 * <p>ut11 ut12
25965 *
25966 * 2450123.7 0.0 (JD method)
25967 * 2451545.0 -1421.3 (J2000 method)
25968 * 2400000.5 50123.2 (MJD method)
25969 * 2450123.5 0.2 (date & time method)
25970 *
25971 * <p>The JD method is the most natural and convenient to use in cases
25972 * where the loss of several decimal digits of resolution is
25973 * acceptable. The J2000 and MJD methods are good compromises
25974 * between resolution and convenience. The date & time method is
25975 * best matched to the algorithm used: maximum precision is
25976 * delivered when the ut11 argument is for 0hrs UT1 on the day in
25977 * question and the ut12 argument lies in the range 0 to 1, or vice
25978 * versa.
25979 *
25980 * <li> If the caller wishes to provide the Earth rotation angle itself,
25981 * the function iauAper can be used instead. One use of this
25982 * technique is to substitute Greenwich apparent sidereal time and
25983 * thereby to support equinox based transformations directly.
25984 *
25985 * <li> This is one of several functions that inserts into the astrom
25986 * structure star-independent parameters needed for the chain of
25987 * astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
25988 *
25989 * <p>The various functions support different classes of observer and
25990 * portions of the transformation chain:
25991 * <pre>{@literal
25992 * functions observer transformation
25993 *
25994 * <p>iauApcg iauApcg13 geocentric ICRS <-> GCRS
25995 * iauApci iauApci13 terrestrial ICRS <-> CIRS
25996 * iauApco iauApco13 terrestrial ICRS <-> observed
25997 * iauApcs iauApcs13 space ICRS <-> GCRS
25998 * iauAper iauAper13 terrestrial update Earth rotation
25999 * iauApio iauApio13 terrestrial CIRS <-> observed
26000 * }</pre>
26001 * <p>Those with names ending in "13" use contemporary SOFA models to
26002 * compute the various ephemerides. The others accept ephemerides
26003 * supplied by the caller.
26004 *
26005 * <p>The transformation from ICRS to GCRS covers space motion,
26006 * parallax, light deflection, and aberration. From GCRS to CIRS
26007 * comprises frame bias and precession-nutation. From CIRS to
26008 * observed takes account of Earth rotation, polar motion, diurnal
26009 * aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
26010 * transformation), and atmospheric refraction.
26011 *
26012 * </ol>
26013 * Called:
26014 * <ul>
26015 * <li>{@link #jauAper} astrometry parameters: update ERA
26016 * <li>{@link #jauEra00} Earth rotation angle, IAU 2000
26017 *
26018 * </ul>
26019 *@version 2013 September 25
26020 *
26021 *@since JSOFA release 20131202
26022 *
26023 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
26024 */
26025 public static void jauAper13(double ut11, double ut12, Astrom astrom)
26026 {
26027 jauAper(jauEra00(ut11,ut12), astrom);
26028
26029 /* Finished. */
26030
26031
26032 }
26033
26034 /**
26035 * For a terrestrial observer, prepare star-independent astrometry
26036 * parameters for transformations between CIRS and observed
26037 * coordinates. The caller supplies the Earth orientation information
26038 * and the refraction constants as well as the site coordinates.
26039 *
26040 *<p>This function is derived from the International Astronomical Union's
26041 * SOFA (Standards of Fundamental Astronomy) software collection.
26042 *
26043 *<p>Status: support function.
26044 *
26045 *<!-- Given: -->
26046 * @param sp double the TIO locator s' (radians, Note 1)
26047 * @param theta double Earth rotation angle (radians)
26048 * @param elong double longitude (radians, east +ve, Note 2)
26049 * @param phi double geodetic latitude (radians, Note 2)
26050 * @param hm double height above ellipsoid (m, geodetic Note 2)
26051 * @param xp double polar motion coordinates (radians, Note 3)
26052 * @param yp double polar motion coordinates (radians, Note 3)
26053 * @param refa double refraction constant A (radians, Note 4)
26054 * @param refb double refraction constant B (radians, Note 4)
26055 *
26056 *<!-- Returned:-->
26057 * @param astrom {@link Astrom} <b>Returned</b> star-independent astrometry parameters:
26058 *
26059 *<p>Notes:
26060 * <ol>
26061 *
26062 * <li> sp, the TIO locator s', is a tiny quantity needed only by the
26063 * most precise applications. It can either be set to zero or
26064 * predicted using the SOFA function iauSp00.
26065 *
26066 * <li> The geographical coordinates are with respect to the WGS84
26067 * reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
26068 * longitude required by the present function is east-positive
26069 * (i.e. right-handed), in accordance with geographical convention.
26070 *
26071 * <li> The polar motion xp,yp can be obtained from IERS bulletins. The
26072 * values are the coordinates (in radians) of the Celestial
26073 * Intermediate Pole with respect to the International Terrestrial
26074 * Reference System (see IERS Conventions 2003), measured along the
26075 * meridians 0 and 90 deg west respectively. For many applications,
26076 * xp and yp can be set to zero.
26077 *
26078 * <p>Internally, the polar motion is stored in a form rotated onto the
26079 * local meridian.
26080 *
26081 * <li> The refraction constants refa and refb are for use in a
26082 * dZ = A*tan(Z)+B*tan^3(Z) model, where Z is the observed
26083 * (i.e. refracted) zenith distance and dZ is the amount of
26084 * refraction.
26085 *
26086 * <li> It is advisable to take great care with units, as even unlikely
26087 * values of the input parameters are accepted and processed in
26088 * accordance with the models used.
26089 *
26090 * <li> In cases where the caller does not wish to provide the Earth
26091 * rotation information and refraction constants, the function
26092 * iauApio13 can be used instead of the present function. This
26093 * starts from UTC and weather readings etc. and computes suitable
26094 * values using other SOFA functions.
26095 *
26096 * <li> This is one of several functions that inserts into the astrom
26097 * structure star-independent parameters needed for the chain of
26098 * astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
26099 *
26100 * <p>The various functions support different classes of observer and
26101 * portions of the transformation chain:
26102 *<pre>{@literal
26103 * functions observer transformation
26104 *
26105 * iauApcg iauApcg13 geocentric ICRS <-> GCRS
26106 * iauApci iauApci13 terrestrial ICRS <-> CIRS
26107 * iauApco iauApco13 terrestrial ICRS <-> observed
26108 * iauApcs iauApcs13 space ICRS <-> GCRS
26109 * iauAper iauAper13 terrestrial update Earth rotation
26110 * iauApio iauApio13 terrestrial CIRS <-> observed
26111 *}</pre>
26112 * <p>Those with names ending in "13" use contemporary SOFA models to
26113 * compute the various ephemerides. The others accept ephemerides
26114 * supplied by the caller.
26115 *
26116 * <p>The transformation from ICRS to GCRS covers space motion,
26117 * parallax, light deflection, and aberration. From GCRS to CIRS
26118 * comprises frame bias and precession-nutation. From CIRS to
26119 * observed takes account of Earth rotation, polar motion, diurnal
26120 * aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
26121 * transformation), and atmospheric refraction.
26122 *
26123 * <li> The context structure astrom produced by this function is used by
26124 * iauAtioq and iauAtoiq.
26125 *
26126 * </ol>
26127 * Called:
26128 * <ul>
26129 * <li>{@link #jauPvtob} position/velocity of terrestrial station
26130 * <li>{@link #jauAper} astrometry parameters: update ERA
26131 *
26132 * </ul>
26133 *@version 2013 October 9
26134 *
26135 *@since JSOFA release 20131202
26136 *
26137 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
26138 * @throws JSOFAInternalError
26139 * @throws JSOFAIllegalParameter
26140 */
26141 public static void jauApio(double sp, double theta,
26142 double elong, double phi, double hm, double xp, double yp,
26143 double refa, double refb,
26144 Astrom astrom) throws JSOFAIllegalParameter, JSOFAInternalError
26145 {
26146 double sl, cl, pv[][];
26147
26148
26149 /* Longitude with adjustment for TIO locator s'. */
26150 astrom.along = elong + sp;
26151
26152 /* Polar motion, rotated onto the local meridian. */
26153 sl = sin(astrom.along);
26154 cl = cos(astrom.along);
26155 astrom.xpl = xp*cl - yp*sl;
26156 astrom.ypl = xp*sl + yp*cl;
26157
26158 /* Functions of latitude. */
26159 astrom.sphi = sin(phi);
26160 astrom.cphi = cos(phi);
26161
26162 /* Observer's geocentric position and velocity (m, m/s, CIRS). */
26163 pv = jauPvtob(elong, phi, hm, xp, yp, sp, theta);
26164
26165 /* Magnitude of diurnal aberration vector. */
26166 astrom.diurab = sqrt(pv[1][0]*pv[1][0]+pv[1][1]*pv[1][1]) / CMPS;
26167
26168 /* Refraction constants. */
26169 astrom.refa = refa;
26170 astrom.refb = refb;
26171
26172 /* Local Earth rotation angle. */
26173 jauAper(theta, astrom);
26174
26175 /* Finished. */
26176
26177
26178 }
26179
26180 /**
26181 * For a terrestrial observer, prepare star-independent astrometry
26182 * parameters for transformations between CIRS and observed
26183 * coordinates. The caller supplies UTC, site coordinates, ambient air
26184 * conditions and observing wavelength.
26185 *
26186 *<p>This function is derived from the International Astronomical Union's
26187 * SOFA (Standards of Fundamental Astronomy) software collection.
26188 *
26189 *<p>Status: support function.
26190 *
26191 *<!-- Given: -->
26192 * @param utc1 double UTC as a 2-part...
26193 * @param utc2 double ...quasi Julian Date (Notes 1,2)
26194 * @param dut1 double UT1-UTC (seconds)
26195 * @param elong double longitude (radians, east +ve, Note 3)
26196 * @param phi double geodetic latitude (radians, Note 3)
26197 * @param hm double height above ellipsoid (m, geodetic Notes 4,6)
26198 * @param xp double polar motion coordinates (radians, Note 5)
26199 * @param yp double polar motion coordinates (radians, Note 5)
26200 * @param phpa double pressure at the observer (hPa = mB, Note 6)
26201 * @param tc double ambient temperature at the observer (deg C)
26202 * @param rh double relative humidity at the observer (range 0-1)
26203 * @param wl double wavelength (micrometers, Note 7)
26204 *
26205 *<!-- Returned:-->
26206 * @param astrom <b>Returned</b> star-independent astrometry parameters:
26207 * @throws JSOFAInternalError
26208 * @throws JSOFAIllegalParameter
26209 *
26210 * int status: <b>Returned</b> +1 = dubious year (Note 2)
26211 * 0 = <b>Returned</b> OK
26212 * -1 = <b>Returned</b> unacceptable date
26213 *
26214 *<p>Notes:
26215 * <ol>
26216 *
26217 * <li> utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
26218 * convenient way between the two arguments, for example where utc1
26219 * is the Julian Day Number and utc2 is the fraction of a day.
26220 *
26221 * <p>However, JD cannot unambiguously represent UTC during a leap
26222 * second unless special measures are taken. The convention in the
26223 * present function is that the JD day represents UTC days whether
26224 * the length is 86399, 86400 or 86401 SI seconds.
26225 *
26226 * <p>Applications should use the function iauDtf2d to convert from
26227 * calendar date and time of day into 2-part quasi Julian Date, as
26228 * it implements the leap-second-ambiguity convention just
26229 * described.
26230 *
26231 * <li> The warning status "dubious year" flags UTCs that predate the
26232 * introduction of the time scale or that are too far in the future
26233 * to be trusted. See iauDat for further details.
26234 *
26235 * <li> UT1-UTC is tabulated in IERS bulletins. It increases by exactly
26236 * one second at the end of each positive UTC leap second,
26237 * introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
26238 * practice is under review, and in the future UT1-UTC may grow
26239 * essentially without limit.
26240 *
26241 * <li> The geographical coordinates are with respect to the WGS84
26242 * reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
26243 * longitude required by the present function is east-positive
26244 * (i.e. right-handed), in accordance with geographical convention.
26245 *
26246 * <li> The polar motion xp,yp can be obtained from IERS bulletins. The
26247 * values are the coordinates (in radians) of the Celestial
26248 * Intermediate Pole with respect to the International Terrestrial
26249 * Reference System (see IERS Conventions 2003), measured along the
26250 * meridians 0 and 90 deg west respectively. For many applications,
26251 * xp and yp can be set to zero.
26252 *
26253 * <p>Internally, the polar motion is stored in a form rotated onto
26254 * the local meridian.
26255 *
26256 * <li> If hm, the height above the ellipsoid of the observing station
26257 * in meters, is not known but phpa, the pressure in hPa (=mB), is
26258 * available, an adequate estimate of hm can be obtained from the
26259 * expression
26260 *
26261 * <p>hm = -29.3 * tsl * log ( phpa / 1013.25 );
26262 *
26263 * <p>where tsl is the approximate sea-level air temperature in K
26264 * (See Astrophysical Quantities, C.W.Allen, 3rd edition, section
26265 * 52). Similarly, if the pressure phpa is not known, it can be
26266 * estimated from the height of the observing station, hm, as
26267 * follows:
26268 *
26269 * <p>phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
26270 *
26271 * <p>Note, however, that the refraction is nearly proportional to the
26272 * pressure and that an accurate phpa value is important for
26273 * precise work.
26274 *
26275 * <li> The argument wl specifies the observing wavelength in
26276 * micrometers. The transition from optical to radio is assumed to
26277 * occur at 100 micrometers (about 3000 GHz).
26278 *
26279 * <li> It is advisable to take great care with units, as even unlikely
26280 * values of the input parameters are accepted and processed in
26281 * accordance with the models used.
26282 *
26283 * <li> In cases where the caller wishes to supply his own Earth
26284 * rotation information and refraction constants, the function
26285 * iauApc can be used instead of the present function.
26286 *
26287 * <li> This is one of several functions that inserts into the astrom
26288 * structure star-independent parameters needed for the chain of
26289 * astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
26290 *
26291 * <p>The various functions support different classes of observer and
26292 * portions of the transformation chain:
26293 * <pre>{@literal
26294 * functions observer transformation
26295 *
26296 * iauApcg iauApcg13 geocentric ICRS <-> GCRS
26297 * iauApci iauApci13 terrestrial ICRS <-> CIRS
26298 * iauApco iauApco13 terrestrial ICRS <-> observed
26299 * iauApcs iauApcs13 space ICRS <-> GCRS
26300 * iauAper iauAper13 terrestrial update Earth rotation
26301 * iauApio iauApio13 terrestrial CIRS <-> observed
26302 * }</pre>
26303 * <p>Those with names ending in "13" use contemporary SOFA models to
26304 * compute the various ephemerides. The others accept ephemerides
26305 * supplied by the caller.
26306 *
26307 * <p>The transformation from ICRS to GCRS covers space motion,
26308 * parallax, light deflection, and aberration. From GCRS to CIRS
26309 * comprises frame bias and precession-nutation. From CIRS to
26310 * observed takes account of Earth rotation, polar motion, diurnal
26311 * aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
26312 * transformation), and atmospheric refraction.
26313 *
26314 * <li> The context structure astrom produced by this function is used
26315 * by iauAtioq and iauAtoiq.
26316 *
26317 * </ol>
26318 * Called:
26319 * <ul>
26320 * <li>{@link #jauUtctai} UTC to TAI
26321 * <li>{@link #jauTaitt} TAI to TT
26322 * <li>{@link #jauUtcut1} UTC to UT1
26323 * <li>{@link #jauSp00} the TIO locator s', IERS 2000
26324 * <li>{@link #jauEra00} Earth rotation angle, IAU 2000
26325 * <li>{@link #jauRefco} refraction constants for given ambient conditions
26326 * <li>{@link #jauApio} astrometry parameters, CIRS-observed
26327 *
26328 * </ul>
26329 *@version 2013 October 9
26330 *
26331 *@since JSOFA release 20131202
26332 *
26333 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
26334 * @throws JSOFAInternalError
26335 * @throws JSOFAIllegalParameter
26336 */
26337 public static void jauApio13(double utc1, double utc2, double dut1,
26338 double elong, double phi, double hm, double xp, double yp,
26339 double phpa, double tc, double rh, double wl,
26340 Astrom astrom) throws JSOFAIllegalParameter, JSOFAInternalError
26341 {
26342 double sp, theta;
26343
26344
26345 /* UTC to other time scales. */
26346 JulianDate tai = jauUtctai(utc1, utc2);
26347 JulianDate tt = jauTaitt(tai.djm0, tai.djm1);
26348 JulianDate ut1 = jauUtcut1(utc1, utc2, dut1);
26349
26350 /* TIO locator s'. */
26351 sp = jauSp00(tt.djm0, tt.djm1);
26352
26353 /* Earth rotation angle. */
26354 theta = jauEra00(ut1.djm0, ut1.djm1);
26355
26356 /* Refraction constants A and B. */
26357 RefCos refco = jauRefco(phpa, tc, rh, wl);
26358
26359 /* CIRS <-> observed astrometry parameters. */
26360 jauApio(sp, theta, elong, phi, hm, xp, yp, refco.a, refco.b, astrom);
26361
26362
26363 /* Finished. */
26364
26365
26366 }
26367
26368 /**
26369 * Transform ICRS star data, epoch J2000.0, to CIRS.
26370 *
26371 *<p>This function is derived from the International Astronomical Union's
26372 * SOFA (Standards of Fundamental Astronomy) software collection.
26373 *
26374 *<p>Status: support function.
26375 *
26376 *<!-- Given: -->
26377 * @param rc double ICRS right ascension at J2000.0 (radians, Note 1)
26378 * @param dc double ICRS declination at J2000.0 (radians, Note 1)
26379 * @param pr double RA proper motion (radians/year; Note 2)
26380 * @param pd double Dec proper motion (radians/year)
26381 * @param px double parallax (arcsec)
26382 * @param rv double radial velocity (km/s, +ve if receding)
26383 * @param date1 double TDB as a 2-part...
26384 * @param date2 double ...Julian Date (Note 3)
26385 *
26386 *<!-- Returned:-->
26387 * @return double* <b>Returned</b> CIRS geocentric RA,Dec (radians)
26388 * eo double* <b>Returned</b> equation of the origins (ERA-GST, Note 5)
26389 *
26390 *<p>Notes:
26391 * <ol>
26392 *
26393 * <li> Star data for an epoch other than J2000.0 (for example from the
26394 * Hipparcos catalog, which has an epoch of J1991.25) will require a
26395 * preliminary call to iauPmsafe before use.
26396 *
26397 * <li> The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
26398 *
26399 * <li> The TDB date date1+date2 is a Julian Date, apportioned in any
26400 * convenient way between the two arguments. For example,
26401 * JD(TDB)=2450123.8g could be expressed in any of these ways, among
26402 * others:
26403 *
26404 * date1 date2
26405 *
26406 * 2450123.8g 0.0 (JD method)
26407 * 2451545.0 -1421.3 (J2000 method)
26408 * 2400000.5 50123.2 (MJD method)
26409 * 2450123.5 0.2 (date & time method)
26410 *
26411 * <p>The JD method is the most natural and convenient to use in cases
26412 * where the loss of several decimal digits of resolution is
26413 * acceptable. The J2000 method is best matched to the way the
26414 * argument is handled internally and will deliver the optimum
26415 * resolution. The MJD method and the date & time methods are both
26416 * good compromises between resolution and convenience. For most
26417 * applications of this function the choice will not be at all
26418 * critical.
26419 *
26420 * <p>TT can be used instead of TDB without any significant impact on
26421 * accuracy.
26422 *
26423 * <li> The available accuracy is better than 1 milliarcsecond, limited
26424 * mainly by the precession-nutation model that is used, namely
26425 * IAU 2000A/2006. Very close to solar system bodies, additional
26426 * errors of up to several milliarcseconds can occur because of
26427 * unmodeled light deflection; however, the Sun's contribution is
26428 * taken into account, to first order. The accuracy limitations of
26429 * the SOFA function iauEpv00 (used to compute Earth position and
26430 * velocity) can contribute aberration errors of up to
26431 * 5 microarcseconds. Light deflection at the Sun's limb is
26432 * uncertain at the 0.4 mas level.
26433 *
26434 * <li> Should the transformation to (equinox based) apparent place be
26435 * required rather than (CIO based) intermediate place, subtract the
26436 * equation of the origins from the returned right ascension:
26437 * RA = RI - EO. (The iauAnp function can then be applied, as
26438 * required, to keep the result in the conventional 0-2pi range.)
26439 *
26440 * </ol>
26441 * Called:
26442 * <ul>
26443 * <li>{@link #jauApci13} astrometry parameters, ICRS-CIRS, 2013
26444 * <li>{@link #jauAtciq} quick ICRS to CIRS
26445 *
26446 * </ul>
26447 *@version 2013 October 9
26448 *
26449 *@since JSOFA release 20131202
26450 *
26451 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
26452 */
26453 public static SphericalCoordinateEO jauAtci13(double rc, double dc,
26454 double pr, double pd, double px, double rv,
26455 double date1, double date2)
26456 {
26457 /* Star-independent astrometry parameters */
26458 Astrom astrom = new Astrom();
26459
26460
26461 /* The transformation parameters. */
26462 double eo = jauApci13(date1, date2, astrom);
26463
26464 /* ICRS (epoch J2000.0) to CIRS. */
26465 SphericalCoordinate co = jauAtciq(rc, dc, pr, pd, px, rv, astrom);
26466
26467 return new SphericalCoordinateEO(co, eo);
26468 /* Finished. */
26469
26470
26471 }
26472
26473 /**
26474 * Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed
26475 * star-independent astrometry parameters.
26476 *
26477 * Use of this function is appropriate when efficiency is important and
26478 * where many star positions are to be transformed for one date. The
26479 * star-independent parameters can be obtained by calling one of the
26480 * functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13].
26481 *
26482 * If the parallax and proper motions are zero the iauAtciqz function
26483 * can be used instead.
26484 *
26485 *<p>This function is derived from the International Astronomical Union's
26486 * SOFA (Standards of Fundamental Astronomy) software collection.
26487 *
26488 *<p>Status: support function.
26489 *
26490 *<!-- Given: -->
26491 * @param rc double ICRS RA,Dec at J2000.0 (radians)
26492 * @param dc double ICRS RA,Dec at J2000.0 (radians)
26493 * @param pr double RA proper motion (radians/year; Note 3)
26494 * @param pd double Dec proper motion (radians/year)
26495 * @param px double parallax (arcsec)
26496 * @param rv double radial velocity (km/s, +ve if receding)
26497 * @param astrom star-independent astrometry parameters:
26498 *
26499 *<!-- Returned:-->
26500 * @return double <b>Returned</b> CIRS RA,Dec (radians)
26501 *
26502 *<p>Notes:
26503 * <ol>
26504 *
26505 * <li> All the vectors are with respect to BCRS axes.
26506 *
26507 * <li> Star data for an epoch other than J2000.0 (for example from the
26508 * Hipparcos catalog, which has an epoch of J1991.25) will require a
26509 * preliminary call to iauPmsafe before use.
26510 *
26511 * <li> The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
26512 *
26513 * </ol>
26514 * Called:
26515 * <ul>
26516 * <li>{@link #jauPmpx} proper motion and parallax
26517 * <li>{@link #jauLdsun} light deflection by the Sun
26518 * <li>{@link #jauAb} stellar aberration
26519 * <li>{@link #jauRxp} product of r-matrix and pv-vector
26520 * <li>{@link #jauC2s} p-vector to spherical
26521 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
26522 *
26523 * </ul>
26524 *@version 2013 October 9
26525 *
26526 *@since JSOFA release 20131202
26527 *
26528 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
26529 */
26530 public static SphericalCoordinate jauAtciq(double rc, double dc,
26531 double pr, double pd, double px, double rv,
26532 Astrom astrom)
26533 {
26534 double pco[], pnat[], ppr[], pi[];
26535
26536
26537 /* Proper motion and parallax, giving BCRS coordinate direction. */
26538 pco = jauPmpx(rc, dc, pr, pd, px, rv, astrom.pmt, astrom.eb);
26539
26540 /* Light deflection by the Sun, giving BCRS natural direction. */
26541 pnat = jauLdsun(pco, astrom.eh, astrom.em);
26542
26543 /* Aberration, giving GCRS proper direction. */
26544 ppr = jauAb(pnat, astrom.v, astrom.em, astrom.bm1);
26545
26546 /* Bias-precession-nutation, giving CIRS proper direction. */
26547 pi = jauRxp(astrom.bpn, ppr);
26548
26549 /* CIRS RA,Dec. */
26550 SphericalCoordinate co = jauC2s(pi);
26551 co.alpha = jauAnp(co.alpha);
26552
26553 return co;
26554 /* Finished. */
26555
26556
26557 }
26558
26559 /**
26560 * Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed
26561 * star-independent astrometry parameters plus a list of light-
26562 * deflecting bodies.
26563 *
26564 * Use of this function is appropriate when efficiency is important and
26565 * where many star positions are to be transformed for one date. The
26566 * star-independent parameters can be obtained by calling one of the
26567 * functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13].
26568 *
26569 *
26570 * If the only light-deflecting body to be taken into account is the
26571 * Sun, the iauAtciq function can be used instead. If in addition the
26572 * parallax and proper motions are zero, the iauAtciqz function can be
26573 * used.
26574 *
26575 *<p>This function is derived from the International Astronomical Union's
26576 * SOFA (Standards of Fundamental Astronomy) software collection.
26577 *
26578 *<p>Status: support function.
26579 *
26580 *<!-- Given: -->
26581 * @param rc double ICRS RA,Dec at J2000.0 (radians)
26582 * @param dc double ICRS RA,Dec at J2000.0 (radians)
26583 * @param pr double RA proper motion (radians/year; Note 3)
26584 * @param pd double Dec proper motion (radians/year)
26585 * @param px double parallax (arcsec)
26586 * @param rv double radial velocity (km/s, +ve if receding)
26587 * @param astrom star-independent astrometry parameters:
26588 * @param n int number of bodies (Note 3)
26589 * @param b jauLDBODY[n] data for each of the n bodies (Notes 3,4):
26590 *
26591 *<!-- Returned:-->
26592 * @return ri,di double <b>Returned</b> CIRS RA,Dec (radians)
26593 *
26594 *<p>Notes:
26595 * <ol>
26596 *
26597 * <li> Star data for an epoch other than J2000.0 (for example from the
26598 * Hipparcos catalog, which has an epoch of J1991.25) will require a
26599 * preliminary call to iauPmsafe before use.
26600 *
26601 * <li> The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
26602 *
26603 * <li> The struct b contains n entries, one for each body to be
26604 * considered. If n = 0, no gravitational light deflection will be
26605 * applied, not even for the Sun.
26606 *
26607 * <li> The struct b should include an entry for the Sun as well as for
26608 * any planet or other body to be taken into account. The entries
26609 * should be in the order in which the light passes the body.
26610 *
26611 * <li> In the entry in the b struct for body i, the mass parameter
26612 * b[i].bm can, as required, be adjusted in order to allow for such
26613 * effects as quadrupole field.
26614 *
26615 * <li> The deflection limiter parameter b[i].dl is phi^2/2, where phi is
26616 * the angular separation (in radians) between star and body at
26617 * which limiting is applied. As phi shrinks below the chosen
26618 * threshold, the deflection is artificially reduced, reaching zero
26619 * for phi = 0. Example values suitable for a terrestrial
26620 * observer, together with masses, are as follows:
26621 * <pre>
26622 * body i b[i].bm b[i].dl
26623 *
26624 * Sun 1.0 6e-6
26625 * Jupiter 0.00095435 3e-9
26626 * Saturn 0.00028574 3e-10
26627 * </pre>
26628 * <li> For efficiency, validation of the contents of the b array is
26629 * omitted. The supplied masses must be greater than zero, the
26630 * position and velocity vectors must be right, and the deflection
26631 * limiter greater than zero.
26632 *
26633 * </ol>
26634 * Called:
26635 * <ul>
26636 * <li>{@link #jauPmpx} proper motion and parallax
26637 * <li>{@link #jauLdn} light deflection by n bodies
26638 * <li>{@link #jauAb} stellar aberration
26639 * <li>{@link #jauRxp} product of r-matrix and pv-vector
26640 * <li>{@link #jauC2s} p-vector to spherical
26641 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
26642 *
26643 * </ul>
26644 *@version 2013 October 9
26645 *
26646 *@since JSOFA release 20131202
26647 *
26648 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
26649 */
26650 public static SphericalCoordinate jauAtciqn(double rc, double dc, double pr, double pd,
26651 double px, double rv, Astrom astrom,
26652 int n, Ldbody b[])
26653 {
26654 double pco[], pnat[], ppr[] = new double[3], pi[] = new double[3];
26655
26656
26657 /* Proper motion and parallax, giving BCRS coordinate direction. */
26658 pco = jauPmpx(rc, dc, pr, pd, px, rv, astrom.pmt, astrom.eb);
26659
26660 /* Light deflection, giving BCRS natural direction. */
26661 pnat = jauLdn(n, b, astrom.eb, pco);
26662
26663 /* Aberration, giving GCRS proper direction. */
26664 ppr = jauAb(pnat, astrom.v, astrom.em, astrom.bm1);
26665
26666 /* Bias-precession-nutation, giving CIRS proper direction. */
26667 pi = jauRxp(astrom.bpn, ppr);
26668
26669 /* CIRS RA,Dec. */
26670 SphericalCoordinate co = jauC2s(pi);
26671 co.alpha = jauAnp(co.alpha);
26672
26673 return co;
26674 /* Finished. */
26675
26676
26677 }
26678
26679 /**
26680 * Quick ICRS to CIRS transformation, given precomputed star-
26681 * independent astrometry parameters, and assuming zero parallax and
26682 * proper motion.
26683 *
26684 * Use of this function is appropriate when efficiency is important and
26685 * where many star positions are to be transformed for one date. The
26686 * star-independent parameters can be obtained by calling one of the
26687 * functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13].
26688 *
26689 * The corresponding function for the case of non-zero parallax and
26690 * proper motion is iauAtciq.
26691 *
26692 *<p>This function is derived from the International Astronomical Union's
26693 * SOFA (Standards of Fundamental Astronomy) software collection.
26694 *
26695 *<p>Status: support function.
26696 *
26697 *<!-- Given: -->
26698 * @param rc double ICRS astrometric RA,Dec (radians)
26699 * @param dc double ICRS astrometric RA,Dec (radians)
26700 * @param astrom star-independent astrometry parameters:
26701 *
26702 *<!-- Returned:-->
26703 * @return ri,di double <b>Returned</b> CIRS RA,Dec (radians)
26704 *
26705 * Note:
26706 *
26707 * @return All the <b>Returned</b> vectors are with respect to BCRS axes.
26708 *
26709 *<p>References:
26710 * <ul>
26711 *
26712 * <li> Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
26713 * the Astronomical Almanac, 3rd ed., University Science Books
26714 * (2013).
26715 *
26716 * <li> Klioner, Sergei A., "A practical relativistic model for micro-
26717 * arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003).
26718 *
26719 * </ul>
26720 * Called:
26721 * <ul>
26722 * <li>{@link #jauS2c} spherical coordinates to unit vector
26723 * <li>{@link #jauLdsun} light deflection due to Sun
26724 * <li>{@link #jauAb} stellar aberration
26725 * <li>{@link #jauRxp} product of r-matrix and p-vector
26726 * <li>{@link #jauC2s} p-vector to spherical
26727 * <li>{@link #jauAnp} normalize angle into range +/- pi
26728 *
26729 * </ul>
26730 *@version 2013 October 9
26731 *
26732 *@since JSOFA release 20131202
26733 *
26734 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
26735 */
26736 public static SphericalCoordinate jauAtciqz(double rc, double dc, Astrom astrom)
26737 {
26738 double pco[], pnat[], ppr[] = new double[3], pi[];
26739
26740
26741 /* BCRS coordinate direction (unit vector). */
26742 pco = jauS2c(rc, dc);
26743
26744 /* Light deflection by the Sun, giving BCRS natural direction. */
26745 pnat = jauLdsun(pco, astrom.eh, astrom.em);
26746
26747 /* Aberration, giving GCRS proper direction. */
26748 ppr = jauAb(pnat, astrom.v, astrom.em, astrom.bm1);
26749
26750 /* Bias-precession-nutation, giving CIRS proper direction. */
26751 pi = jauRxp(astrom.bpn, ppr);
26752
26753 /* CIRS RA,Dec. */
26754 SphericalCoordinate co = jauC2s(pi);
26755 co.alpha = jauAnp(co.alpha);
26756
26757 return co;
26758 /* Finished. */
26759
26760
26761 }
26762
26763 /**
26764 * ICRS RA,Dec to observed place. The caller supplies UTC, site
26765 * coordinates, ambient air conditions and observing wavelength.
26766 *
26767 * SOFA models are used for the Earth ephemeris, bias-precession-
26768 * nutation, Earth orientation and refraction.
26769 *
26770 *<p>This function is derived from the International Astronomical Union's
26771 * SOFA (Standards of Fundamental Astronomy) software collection.
26772 *
26773 *<p>Status: support function.
26774 *
26775 *<!-- Given: -->
26776 * @param rc double ICRS right ascension at J2000.0 (radians, Note 1)
26777 * @param dc double ICRS right ascension at J2000.0 (radians, Note 1)
26778 * @param pr double RA proper motion (radians/year; Note 2)
26779 * @param pd double Dec proper motion (radians/year)
26780 * @param px double parallax (arcsec)
26781 * @param rv double radial velocity (km/s, +ve if receding)
26782 * @param utc1 double UTC as a 2-part...
26783 * @param utc2 double ...quasi Julian Date (Notes 3-4)
26784 * @param dut1 double UT1-UTC (seconds, Note 5)
26785 * @param elong double longitude (radians, east +ve, Note 6)
26786 * @param phi double latitude (geodetic, radians, Note 6)
26787 * @param hm double height above ellipsoid (m, geodetic, Notes 6,8)
26788 * @param xp double polar motion coordinates (radians, Note 7)
26789 * @param yp double polar motion coordinates (radians, Note 7)
26790 * @param phpa double pressure at the observer (hPa = mB, Note 8)
26791 * @param tc double ambient temperature at the observer (deg C)
26792 * @param rh double relative humidity at the observer (range 0-1)
26793 * @param wl double wavelength (micrometers, Note 9)
26794 *
26795 *<!-- Returned:-->
26796 * @return aob double* <b>Returned</b> observed azimuth (radians: N=0,E=90)
26797 * zob double* <b>Returned</b> observed zenith distance (radians)
26798 * hob double* <b>Returned</b> observed hour angle (radians)
26799 * dob double* <b>Returned</b> observed declination (radians)
26800 * rob double* <b>Returned</b> observed right ascension (CIO-based, radians)
26801 * eo double* <b>Returned</b> equation of the origins (ERA-GST)
26802 *
26803 * @throws JSOFAInternalError
26804 * @throws JSOFAIllegalParameter
26805 * int status: <b>Returned</b> +1 = dubious year (Note 4)
26806 * 0 = <b>Returned</b> OK
26807 * -1 = <b>Returned</b> unacceptable date
26808 *
26809 *<p>Notes:
26810 * <ol>
26811 *
26812 * <li> Star data for an epoch other than J2000.0 (for example from the
26813 * Hipparcos catalog, which has an epoch of J1991.25) will require
26814 * a preliminary call to iauPmsafe before use.
26815 *
26816 * <li> The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
26817 *
26818 * <li> utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
26819 * convenient way between the two arguments, for example where utc1
26820 * is the Julian Day Number and utc2 is the fraction of a day.
26821 *
26822 * <p>However, JD cannot unambiguously represent UTC during a leap
26823 * second unless special measures are taken. The convention in the
26824 * present function is that the JD day represents UTC days whether
26825 * the length is 86399, 86400 or 86401 SI seconds.
26826 *
26827 * <p>Applications should use the function iauDtf2d to convert from
26828 * calendar date and time of day into 2-part quasi Julian Date, as
26829 * it implements the leap-second-ambiguity convention just
26830 * described.
26831 *
26832 * <li> The warning status "dubious year" flags UTCs that predate the
26833 * introduction of the time scale or that are too far in the
26834 * future to be trusted. See iauDat for further details.
26835 *
26836 * <li> UT1-UTC is tabulated in IERS bulletins. It increases by exactly
26837 * one second at the end of each positive UTC leap second,
26838 * introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
26839 * practice is under review, and in the future UT1-UTC may grow
26840 * essentially without limit.
26841 *
26842 * <li> The geographical coordinates are with respect to the WGS84
26843 * reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
26844 * longitude required by the present function is east-positive
26845 * (i.e. right-handed), in accordance with geographical convention.
26846 *
26847 * <li> The polar motion xp,yp can be obtained from IERS bulletins. The
26848 * values are the coordinates (in radians) of the Celestial
26849 * Intermediate Pole with respect to the International Terrestrial
26850 * Reference System (see IERS Conventions 2003), measured along the
26851 * meridians 0 and 90 deg west respectively. For many
26852 * applications, xp and yp can be set to zero.
26853 *
26854 * <li> If hm, the height above the ellipsoid of the observing station
26855 * in meters, is not known but phpa, the pressure in hPa (=mB),
26856 * is available, an adequate estimate of hm can be obtained from
26857 * the expression
26858 *
26859 * <p>hm = -29.3 * tsl * log ( phpa / 1013.25 );
26860 *
26861 * <p>where tsl is the approximate sea-level air temperature in K
26862 * (See Astrophysical Quantities, C.W.Allen, 3rd edition, section
26863 * 52). Similarly, if the pressure phpa is not known, it can be
26864 * estimated from the height of the observing station, hm, as
26865 * follows:
26866 *
26867 * <p>phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
26868 *
26869 * <p>Note, however, that the refraction is nearly proportional to
26870 * the pressure and that an accurate phpa value is important for
26871 * precise work.
26872 *
26873 * <li> The argument wl specifies the observing wavelength in
26874 * micrometers. The transition from optical to radio is assumed to
26875 * occur at 100 micrometers (about 3000 GHz).
26876 *
26877 * <li> The accuracy of the result is limited by the corrections for
26878 * refraction, which use a simple A*tan(z) + B*tan^3(z) model.
26879 * Providing the meteorological parameters are known accurately and
26880 * there are no gross local effects, the predicted observed
26881 * coordinates should be within 0.05 arcsec (optical) or 1 arcsec
26882 * (radio) for a zenith distance of less than 70 degrees, better
26883 * than 30 arcsec (optical or radio) at 85 degrees and better
26884 * than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
26885 *
26886 * <p>Without refraction, the complementary functions iauAtco13 and
26887 * iauAtoc13 are self-consistent to better than 1 microarcsecond
26888 * all over the celestial sphere. With refraction included,
26889 * consistency falls off at high zenith distances, but is still
26890 * better than 0.05 arcsec at 85 degrees.
26891 *
26892 * <li> "Observed" Az,ZD means the position that would be seen by a
26893 * perfect geodetically aligned theodolite. (Zenith distance is
26894 * used rather than altitude in order to reflect the fact that no
26895 * allowance is made for depression of the horizon.) This is
26896 * related to the observed HA,Dec via the standard rotation, using
26897 * the geodetic latitude (corrected for polar motion), while the
26898 * observed HA and RA are related simply through the Earth rotation
26899 * angle and the site longitude. "Observed" RA,Dec or HA,Dec thus
26900 * means the position that would be seen by a perfect equatorial
26901 * with its polar axis aligned to the Earth's axis of rotation.
26902 *
26903 * <li> It is advisable to take great care with units, as even unlikely
26904 * values of the input parameters are accepted and processed in
26905 * accordance with the models used.
26906 *
26907 * </ol>
26908 * Called:
26909 * <ul>
26910 * <li>{@link #jauApco13} astrometry parameters, ICRS-observed, 2013
26911 * <li>{@link #jauAtciq} quick ICRS to CIRS
26912 * <li>{@link #jauAtioq} quick ICRS to observed
26913 *
26914 * </ul>
26915 *@version 2013 October 9
26916 *
26917 *@since JSOFA release 20131202
26918 *
26919 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
26920 * @throws JSOFAInternalError
26921 * @throws JSOFAIllegalParameter
26922 */
26923 public static ObservedPositionEO jauAtco13(double rc, double dc,
26924 double pr, double pd, double px, double rv,
26925 double utc1, double utc2, double dut1,
26926 double elong, double phi, double hm, double xp, double yp,
26927 double phpa, double tc, double rh, double wl) throws JSOFAIllegalParameter, JSOFAInternalError
26928 {
26929 Astrom astrom = new Astrom();
26930
26931
26932 /* Star-independent astrometry parameters. */
26933 double eo = jauApco13(utc1, utc2, dut1, elong, phi, hm, xp, yp,
26934 phpa, tc, rh, wl, astrom);
26935
26936 /* Transform ICRS to CIRS. */
26937 SphericalCoordinate co = jauAtciq(rc, dc, pr, pd, px, rv, astrom);
26938
26939 /* Transform CIRS to observed. */
26940 ObservedPosition obs = jauAtioq(co.alpha, co.delta, astrom);
26941
26942
26943 return new ObservedPositionEO(obs, eo);
26944
26945 /* Finished. */
26946
26947
26948 }
26949
26950 /**
26951 * Transform star RA,Dec from geocentric CIRS to ICRS astrometric.
26952 *
26953 *<p>This function is derived from the International Astronomical Union's
26954 * SOFA (Standards of Fundamental Astronomy) software collection.
26955 *
26956 *<p>Status: support function.
26957 *
26958 *<!-- Given: -->
26959 * @param ri double CIRS geocentric RA,Dec (radians)
26960 * @param di double CIRS geocentric RA,Dec (radians)
26961 * @param date1 double TDB as a 2-part...
26962 * @param date2 double ...Julian Date (Note 1)
26963 *
26964 *<!-- Returned:-->
26965 * @return rc,dc double <b>Returned</b> ICRS astrometric RA,Dec (radians)
26966 * eo double <b>Returned</b> equation of the origins (ERA-GST, Note 4)
26967 *
26968 *<p>Notes:
26969 * <ol>
26970 *
26971 * <li> The TDB date date1+date2 is a Julian Date, apportioned in any
26972 * convenient way between the two arguments. For example,
26973 * JD(TDB)=2450123.7 could be expressed in any of these ways, among
26974 * others:
26975 *
26976 * date1 date2
26977 *
26978 * 2450123.7 0.0 (JD method)
26979 * 2451545.0 -1421.3 (J2000 method)
26980 * 2400000.5 50123.2 (MJD method)
26981 * 2450123.5 0.2 (date & time method)
26982 *
26983 * <p>The JD method is the most natural and convenient to use in cases
26984 * where the loss of several decimal digits of resolution is
26985 * acceptable. The J2000 method is best matched to the way the
26986 * argument is handled internally and will deliver the optimum
26987 * resolution. The MJD method and the date & time methods are both
26988 * good compromises between resolution and convenience. For most
26989 * applications of this function the choice will not be at all
26990 * critical.
26991 *
26992 * <p>TT can be used instead of TDB without any significant impact on
26993 * accuracy.
26994 *
26995 * <li> Iterative techniques are used for the aberration and light
26996 * deflection corrections so that the functions iauAtic13 (or
26997 * iauAticq) and iauAtci13 (or iauAtciq) are accurate inverses;
26998 * even at the edge of the Sun's disk the discrepancy is only about
26999 * 1 nanoarcsecond.
27000 *
27001 * <li> The available accuracy is better than 1 milliarcsecond, limited
27002 * mainly by the precession-nutation model that is used, namely
27003 * IAU 2000A/2006. Very close to solar system bodies, additional
27004 * errors of up to several milliarcseconds can occur because of
27005 * unmodeled light deflection; however, the Sun's contribution is
27006 * taken into account, to first order. The accuracy limitations of
27007 * the SOFA function iauEpv00 (used to compute Earth position and
27008 * velocity) can contribute aberration errors of up to
27009 * 5 microarcseconds. Light deflection at the Sun's limb is
27010 * uncertain at the 0.4 mas level.
27011 *
27012 * <li> Should the transformation to (equinox based) J2000.0 mean place
27013 * be required rather than (CIO based) ICRS coordinates, subtract the
27014 * equation of the origins from the returned right ascension:
27015 * RA = RI - EO. (The iauAnp function can then be applied, as
27016 * required, to keep the result in the conventional 0-2pi range.)
27017 *
27018 * </ol>
27019 * Called:
27020 * <ul>
27021 * <li>{@link #jauApci13} astrometry parameters, ICRS-CIRS, 2013
27022 * <li>{@link #jauAticq} quick CIRS to ICRS astrometric
27023 *
27024 * </ul>
27025 *@version 2013 October 9
27026 *
27027 *@since JSOFA release 20131202
27028 *
27029 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
27030 */
27031 public static SphericalCoordinateEO jauAtic13(double ri, double di, double date1, double date2)
27032 {
27033 /* Star-independent astrometry parameters */
27034 Astrom astrom = new Astrom();
27035
27036
27037 /* Star-independent astrometry parameters. */
27038 double eo = jauApci13(date1, date2, astrom);
27039
27040 /* CIRS to ICRS astrometric. */
27041 SphericalCoordinate co = jauAticq(ri, di, astrom);
27042
27043 return new SphericalCoordinateEO(co,eo);
27044 /* Finished. */
27045
27046
27047 }
27048
27049 /**
27050 * Quick CIRS RA,Dec to ICRS astrometric place, given the star-
27051 * independent astrometry parameters.
27052 *
27053 * Use of this function is appropriate when efficiency is important and
27054 * where many star positions are all to be transformed for one date.
27055 * The star-independent astrometry parameters can be obtained by
27056 * calling one of the functions iauApci[13], iauApcg[13], iauApco[13]
27057 * or iauApcs[13].
27058 *
27059 *<p>This function is derived from the International Astronomical Union's
27060 * SOFA (Standards of Fundamental Astronomy) software collection.
27061 *
27062 *<p>Status: support function.
27063 *
27064 *<!-- Given: -->
27065 * @param ri double CIRS RA,Dec (radians)
27066 * @param di double CIRS RA,Dec (radians)
27067 * @param astrom star-independent astrometry parameters:
27068 *
27069 *<!-- Returned:-->
27070 * @return rc,dc double <b>Returned</b> ICRS astrometric RA,Dec (radians)
27071 *
27072 *<p>Notes:
27073 * <ol>
27074 *
27075 * <li> Only the Sun is taken into account in the light deflection
27076 * correction.
27077 *
27078 * <li> Iterative techniques are used for the aberration and light
27079 * deflection corrections so that the functions iauAtic13 (or
27080 * iauAticq) and iauAtci13 (or iauAtciq) are accurate inverses;
27081 * even at the edge of the Sun's disk the discrepancy is only about
27082 * 1 nanoarcsecond.
27083 *
27084 * </ol>
27085 * Called:
27086 * <ul>
27087 * <li>{@link #jauS2c} spherical coordinates to unit vector
27088 * <li>{@link #jauTrxp} product of transpose of r-matrix and p-vector
27089 * <li>{@link #jauZp} zero p-vector
27090 * <li>{@link #jauAb} stellar aberration
27091 * <li>{@link #jauLdsun} light deflection by the Sun
27092 * <li>{@link #jauC2s} p-vector to spherical
27093 * <li>{@link #jauAnp} normalize angle into range +/- pi
27094 *
27095 * </ul>
27096 *@version 2013 October 9
27097 *
27098 *@since JSOFA release 20131202
27099 *
27100 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
27101 */
27102 public static SphericalCoordinate jauAticq(double ri, double di, Astrom astrom )
27103 {
27104 int j, i;
27105 double pi[] , ppr[], pnat[] = new double[3], pco[] = new double[3], w, d[] = new double[3],
27106 before[] = new double[3], r2, r,
27107 after[];
27108
27109
27110 /* CIRS RA,Dec to Cartesian. */
27111 pi = jauS2c(ri, di);
27112
27113 /* Bias-precession-nutation, giving GCRS proper direction. */
27114 ppr = jauTrxp(astrom.bpn, pi);
27115
27116 /* Aberration, giving GCRS natural direction. */
27117 jauZp(d);
27118 for (j = 0; j < 2; j++) {
27119 r2 = 0.0;
27120 for (i = 0; i < 3; i++) {
27121 w = ppr[i] - d[i];
27122 before[i] = w;
27123 r2 += w*w;
27124 }
27125 r = sqrt(r2);
27126 for (i = 0; i < 3; i++) {
27127 before[i] /= r;
27128 }
27129 after = jauAb(before, astrom.v, astrom.em, astrom.bm1);
27130 r2 = 0.0;
27131 for (i = 0; i < 3; i++) {
27132 d[i] = after[i] - before[i];
27133 w = ppr[i] - d[i];
27134 pnat[i] = w;
27135 r2 += w*w;
27136 }
27137 r = sqrt(r2);
27138 for (i = 0; i < 3; i++) {
27139 pnat[i] /= r;
27140 }
27141 }
27142
27143 /* Light deflection by the Sun, giving BCRS coordinate direction. */
27144 jauZp(d);
27145 for (j = 0; j < 5; j++) {
27146 r2 = 0.0;
27147 for (i = 0; i < 3; i++) {
27148 w = pnat[i] - d[i];
27149 before[i] = w;
27150 r2 += w*w;
27151 }
27152 r = sqrt(r2);
27153 for (i = 0; i < 3; i++) {
27154 before[i] /= r;
27155 }
27156 after = jauLdsun(before, astrom.eh, astrom.em);
27157 r2 = 0.0;
27158 for (i = 0; i < 3; i++) {
27159 d[i] = after[i] - before[i];
27160 w = pnat[i] - d[i];
27161 pco[i] = w;
27162 r2 += w*w;
27163 }
27164 r = sqrt(r2);
27165 for (i = 0; i < 3; i++) {
27166 pco[i] /= r;
27167 }
27168 }
27169
27170 /* ICRS astrometric RA,Dec. */
27171 SphericalCoordinate co = jauC2s(pco);
27172 co.alpha = jauAnp(co.alpha);
27173
27174 return co;
27175 /* Finished. */
27176
27177
27178 }
27179
27180 /**
27181 * Quick CIRS to ICRS astrometric place transformation, given the star-
27182 * independent astrometry parameters plus a list of light-deflecting
27183 * bodies.
27184 *
27185 * Use of this function is appropriate when efficiency is important and
27186 * where many star positions are all to be transformed for one date.
27187 * The star-independent astrometry parameters can be obtained by
27188 * calling one of the functions iauApci[13], iauApcg[13], iauApco[13]
27189 * or iauApcs[13].
27190 *
27191 * If the only light-deflecting body to be taken into account is the
27192 * Sun, the iauAticq function can be used instead.
27193 *
27194 *<p>This function is derived from the International Astronomical Union's
27195 * SOFA (Standards of Fundamental Astronomy) software collection.
27196 *
27197 *<p>Status: support function.
27198 *
27199 *<!-- Given: -->
27200 * @param ri double CIRS RA,Dec (radians)
27201 * @param di double CIRS RA,Dec (radians)
27202 * @param astrom star-independent astrometry parameters:
27203 *
27204 *<!-- Returned:-->
27205 * @return rc,dc double <b>Returned</b> ICRS astrometric RA,Dec (radians)
27206 *
27207 *<p>Notes:
27208 * <ol>
27209 *
27210 * <li> Iterative techniques are used for the aberration and light
27211 * deflection corrections so that the functions iauAticqn and
27212 * iauAtciqn are accurate inverses; even at the edge of the Sun's
27213 * disk the discrepancy is only about 1 nanoarcsecond.
27214 *
27215 * <li> If the only light-deflecting body to be taken into account is the
27216 * Sun, the iauAticq function can be used instead.
27217 *
27218 * <li> The struct b contains n entries, one for each body to be
27219 * considered. If n = 0, no gravitational light deflection will be
27220 * applied, not even for the Sun.
27221 *
27222 * <li> The struct b should include an entry for the Sun as well as for
27223 * any planet or other body to be taken into account. The entries
27224 * should be in the order in which the light passes the body.
27225 *
27226 * <li> In the entry in the b struct for body i, the mass parameter
27227 * b[i].bm can, as required, be adjusted in order to allow for such
27228 * effects as quadrupole field.
27229 *
27230 * <li> The deflection limiter parameter b[i].dl is phi^2/2, where phi is
27231 * the angular separation (in radians) between star and body at
27232 * which limiting is applied. As phi shrinks below the chosen
27233 * threshold, the deflection is artificially reduced, reaching zero
27234 * for phi = 0. Example values suitable for a terrestrial
27235 * observer, together with masses, are as follows:
27236 *
27237 * <p>body i b[i].bm b[i].dl
27238 *
27239 * <p>Sun 1.0 6e-6
27240 * Jupiter 0.00095435 3e-9
27241 * Saturn 0.00028574 3e-10
27242 *
27243 * <li> For efficiency, validation of the contents of the b array is
27244 * omitted. The supplied masses must be greater than zero, the
27245 * position and velocity vectors must be right, and the deflection
27246 * limiter greater than zero.
27247 *
27248 * </ol>
27249 * Called:
27250 * <ul>
27251 * <li>{@link #jauS2c} spherical coordinates to unit vector
27252 * <li>{@link #jauTrxp} product of transpose of r-matrix and p-vector
27253 * <li>{@link #jauZp} zero p-vector
27254 * <li>{@link #jauAb} stellar aberration
27255 * <li>{@link #jauLdn} light deflection by n bodies
27256 * <li>{@link #jauC2s} p-vector to spherical
27257 * <li>{@link #jauAnp} normalize angle into range +/- pi
27258 *
27259 * </ul>
27260 *@version 2013 October 9
27261 *
27262 *@since JSOFA release 20131202
27263 *
27264 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
27265 */
27266 public static SphericalCoordinate jauAticqn(double ri, double di, Astrom astrom,
27267 int n, Ldbody b[])
27268 {
27269 int j, i;
27270 double pi[], ppr[], pnat[] = new double[3], pco[] = new double[3], w, d[] = new double[3], before[] = new double[3], r2, r,
27271 after[];
27272
27273
27274 /* CIRS RA,Dec to Cartesian. */
27275 pi = jauS2c(ri, di);
27276
27277 /* Bias-precession-nutation, giving GCRS proper direction. */
27278 ppr = jauTrxp(astrom.bpn, pi);
27279
27280 /* Aberration, giving GCRS natural direction. */
27281 jauZp(d);
27282 for (j = 0; j < 2; j++) {
27283 r2 = 0.0;
27284 for (i = 0; i < 3; i++) {
27285 w = ppr[i] - d[i];
27286 before[i] = w;
27287 r2 += w*w;
27288 }
27289 r = sqrt(r2);
27290 for (i = 0; i < 3; i++) {
27291 before[i] /= r;
27292 }
27293 after = jauAb(before, astrom.v, astrom.em, astrom.bm1);
27294 r2 = 0.0;
27295 for (i = 0; i < 3; i++) {
27296 d[i] = after[i] - before[i];
27297 w = ppr[i] - d[i];
27298 pnat[i] = w;
27299 r2 += w*w;
27300 }
27301 r = sqrt(r2);
27302 for (i = 0; i < 3; i++) {
27303 pnat[i] /= r;
27304 }
27305 }
27306
27307 /* Light deflection, giving BCRS coordinate direction. */
27308 jauZp(d);
27309 for (j = 0; j < 5; j++) {
27310 r2 = 0.0;
27311 for (i = 0; i < 3; i++) {
27312 w = pnat[i] - d[i];
27313 before[i] = w;
27314 r2 += w*w;
27315 }
27316 r = sqrt(r2);
27317 for (i = 0; i < 3; i++) {
27318 before[i] /= r;
27319 }
27320 after = jauLdn(n, b, astrom.eb, before);
27321 r2 = 0.0;
27322 for (i = 0; i < 3; i++) {
27323 d[i] = after[i] - before[i];
27324 w = pnat[i] - d[i];
27325 pco[i] = w;
27326 r2 += w*w;
27327 }
27328 r = sqrt(r2);
27329 for (i = 0; i < 3; i++) {
27330 pco[i] /= r;
27331 }
27332 }
27333
27334 /* ICRS astrometric RA,Dec. */
27335 SphericalCoordinate co = jauC2s(pco);
27336 co.alpha = jauAnp(co.alpha);
27337
27338 return co;
27339 /* Finished. */
27340
27341
27342 }
27343
27344 /**
27345 * Observed Position.
27346 * "Observed" Az,ZD means the position that would be seen by a
27347 * perfect geodetically aligned theodolite. (Zenith distance is
27348 * used rather than altitude in order to reflect the fact that no
27349 * allowance is made for depression of the horizon.) This is
27350 * related to the observed HA,Dec via the standard rotation, using
27351 * the geodetic latitude (corrected for polar motion), while the
27352 * observed HA and RA are related simply through the Earth rotation
27353 * angle and the site longitude. "Observed" RA,Dec or HA,Dec thus
27354 * means the position that would be seen by a perfect equatorial
27355 * with its polar axis aligned to the Earth's axis of rotation..
27356 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 28 Mar 2014
27357 * @version $Revision$ $date$
27358 */
27359 public static class ObservedPosition{
27360 /** observed azimuth (radians: N=0,E=90) */
27361 public double aob;
27362
27363 /** observed zenith distance (radians) */
27364 public double zob;
27365
27366 /** observed Hour Angle (radians) */
27367 public double hob;
27368
27369 /** observed Declination (radians) */
27370 public double dob;
27371
27372 /** observed Right Ascension (radians) */
27373 public double rob;
27374 public ObservedPosition(double aob,
27375 double zob,
27376 double hob,
27377 double dob,
27378 double rob
27379 ) {
27380 this.aob = aob;
27381 this.zob = zob;
27382 this.hob = hob;
27383 this.dob = dob;
27384 this.rob = rob;
27385 }
27386 }
27387
27388 /**
27389 * Observed position with the equation of the origins.
27390 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 29 Mar 2014
27391 * @version $Revision$ $date$
27392 */
27393 public static class ObservedPositionEO {
27394 /**
27395 * observed position.
27396 */
27397 public ObservedPosition op;
27398 /**
27399 * The equation of the origins. The equation of the origins is the distance between the true
27400 * equinox and the celestial intermediate origin and, equivalently,
27401 * the difference between Earth rotation angle and Greenwich
27402 * apparent sidereal time (ERA-GST). It comprises the precession
27403 * (since J2000.0) in right ascension plus the equation of the
27404 * equinoxes (including the small correction terms).
27405 */
27406 public double eo;
27407 /**
27408 * @param op
27409 * @param eo
27410 */
27411 public ObservedPositionEO(ObservedPosition op, double eo) {
27412 this.op = op;
27413 this.eo = eo;
27414 }
27415
27416 }
27417
27418
27419
27420
27421 /**
27422 * CIRS RA,Dec to observed place. The caller supplies UTC, site
27423 * coordinates, ambient air conditions and observing wavelength.
27424 *
27425 *<p>This function is derived from the International Astronomical Union's
27426 * SOFA (Standards of Fundamental Astronomy) software collection.
27427 *
27428 *<p>Status: support function.
27429 *
27430 *<!-- Given: -->
27431 * @param ri double CIRS right ascension (CIO-based, radians)
27432 * @param di double CIRS declination (radians)
27433 * @param utc1 double UTC as a 2-part...
27434 * @param utc2 double ...quasi Julian Date (Notes 1,2)
27435 * @param dut1 double UT1-UTC (seconds, Note 3)
27436 * @param elong double longitude (radians, east +ve, Note 4)
27437 * @param phi double geodetic latitude (radians, Note 4)
27438 * @param hm double height above ellipsoid (m, geodetic Notes 4,6)
27439 * @param xp double polar motion coordinates (radians, Note 5)
27440 * @param yp double polar motion coordinates (radians, Note 5)
27441 * @param phpa double pressure at the observer (hPa = mB, Note 6)
27442 * @param tc double ambient temperature at the observer (deg C)
27443 * @param rh double relative humidity at the observer (range 0-1)
27444 * @param wl double wavelength (micrometers, Note 7)
27445 *
27446 *<!-- Returned:-->
27447 * @return aob double* <b>Returned</b> observed azimuth (radians: N=0,E=90)
27448 * zob double* <b>Returned</b> observed zenith distance (radians)
27449 * hob double* <b>Returned</b> observed hour angle (radians)
27450 * dob double* <b>Returned</b> observed declination (radians)
27451 * rob double* <b>Returned</b> observed right ascension (CIO-based, radians)
27452 *
27453 * @throws JSOFAInternalError
27454 * @throws JSOFAIllegalParameter
27455 * int status: <b>Returned</b> +1 = dubious year (Note 2)
27456 * 0 = <b>Returned</b> OK
27457 * -1 = <b>Returned</b> unacceptable date
27458 *
27459 *<p>Notes:
27460 * <ol>
27461 *
27462 * <li> utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
27463 * convenient way between the two arguments, for example where utc1
27464 * is the Julian Day Number and utc2 is the fraction of a day.
27465 *
27466 * <p>However, JD cannot unambiguously represent UTC during a leap
27467 * second unless special measures are taken. The convention in the
27468 * present function is that the JD day represents UTC days whether
27469 * the length is 86399, 86400 or 86401 SI seconds.
27470 *
27471 * <p>Applications should use the function iauDtf2d to convert from
27472 * calendar date and time of day into 2-part quasi Julian Date, as
27473 * it implements the leap-second-ambiguity convention just
27474 * described.
27475 *
27476 * <li> The warning status "dubious year" flags UTCs that predate the
27477 * introduction of the time scale or that are too far in the
27478 * future to be trusted. See iauDat for further details.
27479 *
27480 * <li> UT1-UTC is tabulated in IERS bulletins. It increases by exactly
27481 * one second at the end of each positive UTC leap second,
27482 * introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
27483 * practice is under review, and in the future UT1-UTC may grow
27484 * essentially without limit.
27485 *
27486 * <li> The geographical coordinates are with respect to the WGS84
27487 * reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
27488 * longitude required by the present function is east-positive
27489 * (i.e. right-handed), in accordance with geographical convention.
27490 *
27491 * <li> The polar motion xp,yp can be obtained from IERS bulletins. The
27492 * values are the coordinates (in radians) of the Celestial
27493 * Intermediate Pole with respect to the International Terrestrial
27494 * Reference System (see IERS Conventions 2003), measured along the
27495 * meridians 0 and 90 deg west respectively. For many
27496 * applications, xp and yp can be set to zero.
27497 *
27498 * <li> If hm, the height above the ellipsoid of the observing station
27499 * in meters, is not known but phpa, the pressure in hPa (=mB), is
27500 * available, an adequate estimate of hm can be obtained from the
27501 * expression
27502 *
27503 * <p>hm = -29.3 * tsl * log ( phpa / 1013.25 );
27504 *
27505 * <p>where tsl is the approximate sea-level air temperature in K
27506 * (See Astrophysical Quantities, C.W.Allen, 3rd edition, section
27507 * 52). Similarly, if the pressure phpa is not known, it can be
27508 * estimated from the height of the observing station, hm, as
27509 * follows:
27510 *
27511 * <p>phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
27512 *
27513 * <p>Note, however, that the refraction is nearly proportional to
27514 * the pressure and that an accurate phpa value is important for
27515 * precise work.
27516 *
27517 * <li> The argument wl specifies the observing wavelength in
27518 * micrometers. The transition from optical to radio is assumed to
27519 * occur at 100 micrometers (about 3000 GHz).
27520 *
27521 * <li> "Observed" Az,ZD means the position that would be seen by a
27522 * perfect geodetically aligned theodolite. (Zenith distance is
27523 * used rather than altitude in order to reflect the fact that no
27524 * allowance is made for depression of the horizon.) This is
27525 * related to the observed HA,Dec via the standard rotation, using
27526 * the geodetic latitude (corrected for polar motion), while the
27527 * observed HA and RA are related simply through the Earth rotation
27528 * angle and the site longitude. "Observed" RA,Dec or HA,Dec thus
27529 * means the position that would be seen by a perfect equatorial
27530 * with its polar axis aligned to the Earth's axis of rotation.
27531 *
27532 * <li> The accuracy of the result is limited by the corrections for
27533 * refraction, which use a simple A*tan(z) + B*tan^3(z) model.
27534 * Providing the meteorological parameters are known accurately and
27535 * there are no gross local effects, the predicted astrometric
27536 * coordinates should be within 0.05 arcsec (optical) or 1 arcsec
27537 * (radio) for a zenith distance of less than 70 degrees, better
27538 * than 30 arcsec (optical or radio) at 85 degrees and better
27539 * than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
27540 *
27541 * <li> The complementary functions iauAtio13 and iauAtoi13 are self-
27542 * consistent to better than 1 microarcsecond all over the
27543 * celestial sphere.
27544 *
27545 * <li> It is advisable to take great care with units, as even unlikely
27546 * values of the input parameters are accepted and processed in
27547 * accordance with the models used.
27548 *
27549 * </ol>
27550 * Called:
27551 * <ul>
27552 * <li>{@link #jauApio13} astrometry parameters, CIRS-observed, 2013
27553 * <li>{@link #jauAtioq} quick CIRS to observed
27554 *
27555 * </ul>
27556 *@version 2013 October 9
27557 *
27558 *@since JSOFA release 20131202
27559 *
27560 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
27561 * @throws JSOFAInternalError
27562 * @throws JSOFAIllegalParameter
27563 */
27564 public static ObservedPosition jauAtio13(double ri, double di,
27565 double utc1, double utc2, double dut1,
27566 double elong, double phi, double hm, double xp, double yp,
27567 double phpa, double tc, double rh, double wl) throws JSOFAIllegalParameter, JSOFAInternalError
27568 {
27569 Astrom astrom = new Astrom();
27570
27571
27572 /* Star-independent astrometry parameters for CIRS->observed. */
27573 jauApio13(utc1, utc2, dut1, elong, phi, hm, xp, yp,
27574 phpa, tc, rh, wl, astrom);
27575
27576 /* Transform CIRS to observed. */
27577 return jauAtioq(ri, di, astrom);
27578
27579 /* Finished. */
27580
27581
27582 }
27583
27584 /**
27585 * Quick CIRS to observed place transformation.
27586 *
27587 * Use of this function is appropriate when efficiency is important and
27588 * where many star positions are all to be transformed for one date.
27589 * The star-independent astrometry parameters can be obtained by
27590 * calling iauApio[13] or iauApco[13].
27591 *
27592 *<p>This function is derived from the International Astronomical Union's
27593 * SOFA (Standards of Fundamental Astronomy) software collection.
27594 *
27595 *<p>Status: support function.
27596 *
27597 *<!-- Given: -->
27598 * @param ri double CIRS right ascension
27599 * @param di double CIRS declination
27600 * @param astrom star-independent astrometry parameters:
27601 *
27602 *<!-- Returned:-->
27603 * @return aob double* <b>Returned</b> observed azimuth (radians: N=0,E=90)
27604 * zob double* <b>Returned</b> observed zenith distance (radians)
27605 * hob double* <b>Returned</b> observed hour angle (radians)
27606 * dob double* <b>Returned</b> observed declination (radians)
27607 * rob double* <b>Returned</b> observed right ascension (CIO-based, radians)
27608 *
27609 *<p>Notes:
27610 * <ol>
27611 *
27612 * <li> This function returns zenith distance rather than altitude in
27613 * order to reflect the fact that no allowance is made for
27614 * depression of the horizon.
27615 *
27616 * <li> The accuracy of the result is limited by the corrections for
27617 * refraction, which use a simple A*tan(z) + B*tan^3(z) model.
27618 * Providing the meteorological parameters are known accurately and
27619 * there are no gross local effects, the predicted observed
27620 * coordinates should be within 0.05 arcsec (optical) or 1 arcsec
27621 * (radio) for a zenith distance of less than 70 degrees, better
27622 * than 30 arcsec (optical or radio) at 85 degrees and better
27623 * than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
27624 *
27625 * <p>Without refraction, the complementary functions iauAtioq and
27626 * iauAtoiq are self-consistent to better than 1 microarcsecond all
27627 * over the celestial sphere. With refraction included, consistency
27628 * falls off at high zenith distances, but is still better than
27629 * 0.05 arcsec at 85 degrees.
27630 *
27631 * <li> It is advisable to take great care with units, as even unlikely
27632 * values of the input parameters are accepted and processed in
27633 * accordance with the models used.
27634 *
27635 * <li> The CIRS RA,Dec is obtained from a star catalog mean place by
27636 * allowing for space motion, parallax, the Sun's gravitational lens
27637 * effect, annual aberration and precession-nutation. For star
27638 * positions in the ICRS, these effects can be applied by means of
27639 * the iauAtci13 (etc.) functions. Starting from classical "mean
27640 * place" systems, additional transformations will be needed first.
27641 *
27642 * <li> "Observed" Az,El means the position that would be seen by a
27643 * perfect geodetically aligned theodolite. This is obtained from
27644 * the CIRS RA,Dec by allowing for Earth orientation and diurnal
27645 * aberration, rotating from equator to horizon coordinates, and
27646 * then adjusting for refraction. The HA,Dec is obtained by
27647 * rotating back into equatorial coordinates, and is the position
27648 * that would be seen by a perfect equatorial with its polar axis
27649 * aligned to the Earth's axis of rotation. Finally, the RA is
27650 * obtained by subtracting the HA from the local ERA.
27651 *
27652 * <li> The star-independent CIRS-to-observed-place parameters in ASTROM
27653 * may be computed with iauApio[13] or iauApco[13]. If nothing has
27654 * changed significantly except the time, iauAper[13] may be used to
27655 * perform the requisite adjustment to the astrom structure.
27656 *
27657 * </ol>
27658 * Called:
27659 * <ul>
27660 * <li>{@link #jauS2c} spherical coordinates to unit vector
27661 * <li>{@link #jauC2s} p-vector to spherical
27662 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
27663 *
27664 * </ul>
27665 *@version 2013 December 5
27666 *
27667 *@since JSOFA release 20131202
27668 *
27669 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
27670 */
27671 public static ObservedPosition jauAtioq(double ri, double di, Astrom astrom)
27672 {
27673 /* Minimum cos(alt) and sin(alt) for refraction purposes */
27674 final double CELMIN = 1e-6;
27675 final double SELMIN = 0.05;
27676
27677 double v[] = new double[3], x, y, z, xhd, yhd, zhd, f, xhdt, yhdt, zhdt,
27678 xaet, yaet, zaet, azobs, r, tz, w, del, cosdel,
27679 xaeo, yaeo, zaeo, zdobs, hmobs, dcobs, raobs;
27680
27681 /*--------------------------------------------------------------------*/
27682
27683 /* CIRS RA,Dec to Cartesian -HA,Dec. */
27684 v = jauS2c(ri-astrom.eral, di);
27685 x = v[0];
27686 y = v[1];
27687 z = v[2];
27688
27689 /* Polar motion. */
27690 xhd = x + astrom.xpl*z;
27691 yhd = y - astrom.ypl*z;
27692 zhd = z - astrom.xpl*x + astrom.ypl*y;
27693
27694 /* Diurnal aberration. */
27695 f = ( 1.0 - astrom.diurab*yhd );
27696 xhdt = f * xhd;
27697 yhdt = f * ( yhd + astrom.diurab );
27698 zhdt = f * zhd;
27699
27700 /* Cartesian -HA,Dec to Cartesian Az,El (S=0,E=90). */
27701 xaet = astrom.sphi*xhdt - astrom.cphi*zhdt;
27702 yaet = yhdt;
27703 zaet = astrom.cphi*xhdt + astrom.sphi*zhdt;
27704
27705 /* Azimuth (N=0,E=90). */
27706 azobs = ( xaet != 0.0 || yaet != 0.0 ) ? atan2(yaet,-xaet) : 0.0;
27707
27708 /* ---------- */
27709 /* Refraction */
27710 /* ---------- */
27711
27712 /* Cosine and sine of altitude, with precautions. */
27713 r = sqrt(xaet*xaet + yaet*yaet);
27714 r = r > CELMIN ? r : CELMIN;
27715 z = zaet > SELMIN ? zaet : SELMIN;
27716
27717 /* A*tan(z)+B*tan^3(z) model, with Newton-Raphson correction. */
27718 tz = r/z;
27719 w = astrom.refb*tz*tz;
27720 del = ( astrom.refa + w ) * tz /
27721 ( 1.0 + ( astrom.refa + 3.0*w ) / ( z*z ) );
27722
27723 /* Apply the change, giving observed vector. */
27724 cosdel = 1.0 - del*del/2.0;
27725 f = cosdel - del*z/r;
27726 xaeo = xaet*f;
27727 yaeo = yaet*f;
27728 zaeo = cosdel*zaet + del*r;
27729
27730 /* Observed ZD. */
27731 zdobs = atan2(sqrt(xaeo*xaeo+yaeo*yaeo), zaeo);
27732
27733 /* Az/El vector to HA,Dec vector (both right-handed). */
27734 v[0] = astrom.sphi*xaeo + astrom.cphi*zaeo;
27735 v[1] = yaeo;
27736 v[2] = - astrom.cphi*xaeo + astrom.sphi*zaeo;
27737
27738 /* To spherical -HA,Dec. */
27739 SphericalCoordinate co = jauC2s ( v);
27740 hmobs = co.alpha;
27741 dcobs = co.delta;
27742 /* Right ascension (with respect to CIO). */
27743 raobs = astrom.eral + hmobs;
27744
27745 /* Return the results. */
27746 return new ObservedPosition(
27747 jauAnp(azobs),
27748 zdobs,
27749 -hmobs,
27750 dcobs,
27751 jauAnp(raobs));
27752
27753 /* Finished. */
27754
27755
27756 }
27757
27758 /**
27759 * Observed place at a groundbased site to to ICRS astrometric RA,Dec.
27760 * The caller supplies UTC, site coordinates, ambient air conditions
27761 * and observing wavelength.
27762 *
27763 *<p>This function is derived from the International Astronomical Union's
27764 * SOFA (Standards of Fundamental Astronomy) software collection.
27765 *
27766 *<p>Status: support function.
27767 *
27768 *<!-- Given: -->
27769 * @param type char[] type of coordinates - "R", "H" or "A" (Notes 1,2)
27770 * @param ob1 double observed Az, HA or RA (radians; Az is N=0,E=90)
27771 * @param ob2 double observed ZD or Dec (radians)
27772 * @param utc1 double UTC as a 2-part...
27773 * @param utc2 double ...quasi Julian Date (Notes 3,4)
27774 * @param dut1 double UT1-UTC (seconds, Note 5)
27775 * @param elong double longitude (radians, east +ve, Note 6)
27776 * @param phi double geodetic latitude (radians, Note 6)
27777 * @param hm double height above ellipsoid (m, geodetic Notes 6,8)
27778 * @param xp double polar motion coordinates (radians, Note 7)
27779 * @param yp double polar motion coordinates (radians, Note 7)
27780 * @param phpa double pressure at the observer (hPa = mB, Note 8)
27781 * @param tc double ambient temperature at the observer (deg C)
27782 * @param rh double relative humidity at the observer (range 0-1)
27783 * @param wl double wavelength (micrometers, Note 9)
27784 *
27785 *<!-- Returned:-->
27786 * @return rc,dc double <b>Returned</b> ICRS astrometric RA,Dec (radians)
27787 *
27788 * @throws JSOFAInternalError
27789 * @throws JSOFAIllegalParameter
27790 * int status: <b>Returned</b> +1 = dubious year (Note 4)
27791 * 0 = <b>Returned</b> OK
27792 * -1 = <b>Returned</b> unacceptable date
27793 *
27794 *<p>Notes:
27795 * <ol>
27796 *
27797 * <li> "Observed" Az,ZD means the position that would be seen by a
27798 * perfect geodetically aligned theodolite. (Zenith distance is
27799 * used rather than altitude in order to reflect the fact that no
27800 * allowance is made for depression of the horizon.) This is
27801 * related to the observed HA,Dec via the standard rotation, using
27802 * the geodetic latitude (corrected for polar motion), while the
27803 * observed HA and RA are related simply through the Earth rotation
27804 * angle and the site longitude. "Observed" RA,Dec or HA,Dec thus
27805 * means the position that would be seen by a perfect equatorial
27806 * with its polar axis aligned to the Earth's axis of rotation.
27807 *
27808 * <li> Only the first character of the type argument is significant.
27809 * "R" or "r" indicates that ob1 and ob2 are the observed right
27810 * ascension and declination; "H" or "h" indicates that they are
27811 * hour angle (west +ve) and declination; anything else ("A" or
27812 * "a" is recommended) indicates that ob1 and ob2 are azimuth
27813 * (north zero, east 90 deg) and zenith distance.
27814 *
27815 * <li> utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
27816 * convenient way between the two arguments, for example where utc1
27817 * is the Julian Day Number and utc2 is the fraction of a day.
27818 *
27819 * <p>However, JD cannot unambiguously represent UTC during a leap
27820 * second unless special measures are taken. The convention in the
27821 * present function is that the JD day represents UTC days whether
27822 * the length is 86399, 86400 or 86401 SI seconds.
27823 *
27824 * <p>Applications should use the function iauDtf2d to convert from
27825 * calendar date and time of day into 2-part quasi Julian Date, as
27826 * it implements the leap-second-ambiguity convention just
27827 * described.
27828 *
27829 * <li> The warning status "dubious year" flags UTCs that predate the
27830 * introduction of the time scale or that are too far in the
27831 * future to be trusted. See iauDat for further details.
27832 *
27833 * <li> UT1-UTC is tabulated in IERS bulletins. It increases by exactly
27834 * one second at the end of each positive UTC leap second,
27835 * introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
27836 * practice is under review, and in the future UT1-UTC may grow
27837 * essentially without limit.
27838 *
27839 * <li> The geographical coordinates are with respect to the WGS84
27840 * reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
27841 * longitude required by the present function is east-positive
27842 * (i.e. right-handed), in accordance with geographical convention.
27843 *
27844 * <li> The polar motion xp,yp can be obtained from IERS bulletins. The
27845 * values are the coordinates (in radians) of the Celestial
27846 * Intermediate Pole with respect to the International Terrestrial
27847 * Reference System (see IERS Conventions 2003), measured along the
27848 * meridians 0 and 90 deg west respectively. For many
27849 * applications, xp and yp can be set to zero.
27850 *
27851 * <li> If hm, the height above the ellipsoid of the observing station
27852 * in meters, is not known but phpa, the pressure in hPa (=mB), is
27853 * available, an adequate estimate of hm can be obtained from the
27854 * expression
27855 *
27856 * <p>hm = -29.3 * tsl * log ( phpa / 1013.25 );
27857 *
27858 * <p>where tsl is the approximate sea-level air temperature in K
27859 * (See Astrophysical Quantities, C.W.Allen, 3rd edition, section
27860 * 52). Similarly, if the pressure phpa is not known, it can be
27861 * estimated from the height of the observing station, hm, as
27862 * follows:
27863 *
27864 * <p>phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
27865 *
27866 * <p>Note, however, that the refraction is nearly proportional to
27867 * the pressure and that an accurate phpa value is important for
27868 * precise work.
27869 *
27870 * <li> The argument wl specifies the observing wavelength in
27871 * micrometers. The transition from optical to radio is assumed to
27872 * occur at 100 micrometers (about 3000 GHz).
27873 *
27874 * <li> The accuracy of the result is limited by the corrections for
27875 * refraction, which use a simple A*tan(z) + B*tan^3(z) model.
27876 * Providing the meteorological parameters are known accurately and
27877 * there are no gross local effects, the predicted astrometric
27878 * coordinates should be within 0.05 arcsec (optical) or 1 arcsec
27879 * (radio) for a zenith distance of less than 70 degrees, better
27880 * than 30 arcsec (optical or radio) at 85 degrees and better
27881 * than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
27882 *
27883 * <p>Without refraction, the complementary functions iauAtco13 and
27884 * iauAtoc13 are self-consistent to better than 1 microarcsecond
27885 * all over the celestial sphere. With refraction included,
27886 * consistency falls off at high zenith distances, but is still
27887 * better than 0.05 arcsec at 85 degrees.
27888 *
27889 * <li> It is advisable to take great care with units, as even unlikely
27890 * values of the input parameters are accepted and processed in
27891 * accordance with the models used.
27892 *
27893 * </ol>
27894 * Called:
27895 * <ul>
27896 * <li>{@link #jauApco13} astrometry parameters, ICRS-observed
27897 * <li>{@link #jauAtoiq} quick observed to CIRS
27898 * <li>{@link #jauAticq} quick CIRS to ICRS
27899 *
27900 * </ul>
27901 *@version 2013 October 9
27902 *
27903 *@since JSOFA release 20131202
27904 *
27905 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
27906 * @throws JSOFAInternalError
27907 * @throws JSOFAIllegalParameter
27908 */
27909 public static SphericalCoordinate jauAtoc13(String type, double ob1, double ob2,
27910 double utc1, double utc2, double dut1,
27911 double elong, double phi, double hm, double xp, double yp,
27912 double phpa, double tc, double rh, double wl
27913 ) throws JSOFAIllegalParameter, JSOFAInternalError
27914 {
27915 Astrom astrom = new Astrom();
27916 jauApco13(utc1, utc2, dut1, elong, phi, hm, xp, yp,
27917 phpa, tc, rh, wl, astrom);
27918
27919 /* Transform observed to CIRS. */
27920 SphericalCoordinate co = jauAtoiq(type, ob1, ob2, astrom);
27921
27922 /* Transform CIRS to ICRS. */
27923 SphericalCoordinate icrs = jauAticq(co.alpha, co.delta, astrom);
27924 return icrs;
27925
27926
27927 /* Finished. */
27928
27929
27930 }
27931
27932 /**
27933 * Observed place to CIRS. The caller supplies UTC, site coordinates,
27934 * ambient air conditions and observing wavelength.
27935 *
27936 *<p>This function is derived from the International Astronomical Union's
27937 * SOFA (Standards of Fundamental Astronomy) software collection.
27938 *
27939 *<p>Status: support function.
27940 *
27941 *<!-- Given: -->
27942 * @param type char[] type of coordinates - "R", "H" or "A" (Notes 1,2)
27943 * @param ob1 double observed Az, HA or RA (radians; Az is N=0,E=90)
27944 * @param ob2 double observed ZD or Dec (radians)
27945 * @param utc1 double UTC as a 2-part...
27946 * @param utc2 double ...quasi Julian Date (Notes 3,4)
27947 * @param dut1 double UT1-UTC (seconds, Note 5)
27948 * @param elong double longitude (radians, east +ve, Note 6)
27949 * @param phi double geodetic latitude (radians, Note 6)
27950 * @param hm double height above the ellipsoid (meters, Notes 6,8)
27951 * @param xp double polar motion coordinates (radians, Note 7)
27952 * @param yp double polar motion coordinates (radians, Note 7)
27953 * @param phpa double pressure at the observer (hPa = mB, Note 8)
27954 * @param tc double ambient temperature at the observer (deg C)
27955 * @param rh double relative humidity at the observer (range 0-1)
27956 * @param wl double wavelength (micrometers, Note 9)
27957 *
27958 *<!-- Returned:-->
27959 * @return ri double* <b>Returned</b> CIRS right ascension (CIO-based, radians)
27960 * di double* <b>Returned</b> CIRS declination (radians)
27961 *
27962 * @throws JSOFAInternalError
27963 * @throws JSOFAIllegalParameter
27964 * int status: <b>Returned</b> +1 = dubious year (Note 2)
27965 * 0 = <b>Returned</b> OK
27966 * -1 = <b>Returned</b> unacceptable date
27967 *
27968 *<p>Notes:
27969 * <ol>
27970 *
27971 * <li> "Observed" Az,ZD means the position that would be seen by a
27972 * perfect geodetically aligned theodolite. (Zenith distance is
27973 * used rather than altitude in order to reflect the fact that no
27974 * allowance is made for depression of the horizon.) This is
27975 * related to the observed HA,Dec via the standard rotation, using
27976 * the geodetic latitude (corrected for polar motion), while the
27977 * observed HA and RA are related simply through the Earth rotation
27978 * angle and the site longitude. "Observed" RA,Dec or HA,Dec thus
27979 * means the position that would be seen by a perfect equatorial
27980 * with its polar axis aligned to the Earth's axis of rotation.
27981 *
27982 * <li> Only the first character of the type argument is significant.
27983 * "R" or "r" indicates that ob1 and ob2 are the observed right
27984 * ascension and declination; "H" or "h" indicates that they are
27985 * hour angle (west +ve) and declination; anything else ("A" or
27986 * "a" is recommended) indicates that ob1 and ob2 are azimuth
27987 * (north zero, east 90 deg) and zenith distance.
27988 *
27989 * <li> utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
27990 * convenient way between the two arguments, for example where utc1
27991 * is the Julian Day Number and utc2 is the fraction of a day.
27992 *
27993 * <p>However, JD cannot unambiguously represent UTC during a leap
27994 * second unless special measures are taken. The convention in the
27995 * present function is that the JD day represents UTC days whether
27996 * the length is 86399, 86400 or 86401 SI seconds.
27997 *
27998 * <p>Applications should use the function iauDtf2d to convert from
27999 * calendar date and time of day into 2-part quasi Julian Date, as
28000 * it implements the leap-second-ambiguity convention just
28001 * described.
28002 *
28003 * <li> The warning status "dubious year" flags UTCs that predate the
28004 * introduction of the time scale or that are too far in the
28005 * future to be trusted. See iauDat for further details.
28006 *
28007 * <li> UT1-UTC is tabulated in IERS bulletins. It increases by exactly
28008 * one second at the end of each positive UTC leap second,
28009 * introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
28010 * practice is under review, and in the future UT1-UTC may grow
28011 * essentially without limit.
28012 *
28013 * <li> The geographical coordinates are with respect to the WGS84
28014 * reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
28015 * longitude required by the present function is east-positive
28016 * (i.e. right-handed), in accordance with geographical convention.
28017 *
28018 * <li> The polar motion xp,yp can be obtained from IERS bulletins. The
28019 * values are the coordinates (in radians) of the Celestial
28020 * Intermediate Pole with respect to the International Terrestrial
28021 * Reference System (see IERS Conventions 2003), measured along the
28022 * meridians 0 and 90 deg west respectively. For many
28023 * applications, xp and yp can be set to zero.
28024 *
28025 * <li> If hm, the height above the ellipsoid of the observing station
28026 * in meters, is not known but phpa, the pressure in hPa (=mB), is
28027 * available, an adequate estimate of hm can be obtained from the
28028 * expression
28029 *
28030 * <p>hm = -29.3 * tsl * log ( phpa / 1013.25 );
28031 *
28032 * <p>where tsl is the approximate sea-level air temperature in K
28033 * (See Astrophysical Quantities, C.W.Allen, 3rd edition, section
28034 * 52). Similarly, if the pressure phpa is not known, it can be
28035 * estimated from the height of the observing station, hm, as
28036 * follows:
28037 *
28038 * <p>phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
28039 *
28040 * <p>Note, however, that the refraction is nearly proportional to
28041 * the pressure and that an accurate phpa value is important for
28042 * precise work.
28043 *
28044 * <li> The argument wl specifies the observing wavelength in
28045 * micrometers. The transition from optical to radio is assumed to
28046 * occur at 100 micrometers (about 3000 GHz).
28047 *
28048 * <li> The accuracy of the result is limited by the corrections for
28049 * refraction, which use a simple A*tan(z) + B*tan^3(z) model.
28050 * Providing the meteorological parameters are known accurately and
28051 * there are no gross local effects, the predicted astrometric
28052 * coordinates should be within 0.05 arcsec (optical) or 1 arcsec
28053 * (radio) for a zenith distance of less than 70 degrees, better
28054 * than 30 arcsec (optical or radio) at 85 degrees and better
28055 * than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
28056 *
28057 * <p>Without refraction, the complementary functions iauAtio13 and
28058 * iauAtoi13 are self-consistent to better than 1 microarcsecond
28059 * all over the celestial sphere. With refraction included,
28060 * consistency falls off at high zenith distances, but is still
28061 * better than 0.05 arcsec at 85 degrees.
28062 *
28063 * <li> It is advisable to take great care with units, as even unlikely
28064 * values of the input parameters are accepted and processed in
28065 * accordance with the models used.
28066 *
28067 * </ol>
28068 * Called:
28069 * <ul>
28070 * <li>{@link #jauApio13} astrometry parameters, CIRS-observed, 2013
28071 * <li>{@link #jauAtoiq} quick observed to CIRS
28072 *
28073 * </ul>
28074 *@version 2013 October 9
28075 *
28076 *@since JSOFA release 20131202
28077 *
28078 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
28079 * @throws JSOFAInternalError
28080 * @throws JSOFAIllegalParameter
28081 */
28082 public static SphericalCoordinate jauAtoi13(String type, double ob1, double ob2,
28083 double utc1, double utc2, double dut1,
28084 double elong, double phi, double hm, double xp, double yp,
28085 double phpa, double tc, double rh, double wl
28086 ) throws JSOFAIllegalParameter, JSOFAInternalError
28087 {
28088 Astrom astrom = new Astrom();
28089
28090
28091 /* Star-independent astrometry parameters for CIRS->observed. */
28092 jauApio13(utc1, utc2, dut1, elong, phi, hm, xp, yp,
28093 phpa, tc, rh, wl, astrom);
28094
28095 /* Transform observed to CIRS. */
28096 SphericalCoordinate co = jauAtoiq(type, ob1, ob2, astrom);
28097 return co;
28098
28099 /* Finished. */
28100
28101
28102 }
28103
28104 /**
28105 * Quick observed place to CIRS, given the star-independent astrometry
28106 * parameters.
28107 *
28108 * Use of this function is appropriate when efficiency is important and
28109 * where many star positions are all to be transformed for one date.
28110 * The star-independent astrometry parameters can be obtained by
28111 * calling iauApio[13] or iauApco[13].
28112 *
28113 *<p>Status: support function.
28114 *
28115 *<!-- Given: -->
28116 * @param type char[] type of coordinates: "R", "H" or "A" (Note 1)
28117 * @param ob1 double observed Az, HA or RA (radians; Az is N=0,E=90)
28118 * @param ob2 double observed ZD or Dec (radians)
28119 * @param astrom star-independent astrometry parameters:
28120 *
28121 *<!-- Returned:-->
28122 * @return ri double* <b>Returned</b> CIRS right ascension (CIO-based, radians)
28123 * di double* <b>Returned</b> CIRS declination (radians)
28124 *
28125 *<p>Notes:
28126 * <ol>
28127 *
28128 * <li> "Observed" Az,El means the position that would be seen by a
28129 * perfect geodetically aligned theodolite. This is related to
28130 * the observed HA,Dec via the standard rotation, using the geodetic
28131 * latitude (corrected for polar motion), while the observed HA and
28132 * RA are related simply through the Earth rotation angle and the
28133 * site longitude. "Observed" RA,Dec or HA,Dec thus means the
28134 * position that would be seen by a perfect equatorial with its
28135 * polar axis aligned to the Earth's axis of rotation. By removing
28136 * from the observed place the effects of atmospheric refraction and
28137 * diurnal aberration, the CIRS RA,Dec is obtained.
28138 *
28139 * <li> Only the first character of the type argument is significant.
28140 * "R" or "r" indicates that ob1 and ob2 are the observed right
28141 * ascension and declination; "H" or "h" indicates that they are
28142 * hour angle (west +ve) and declination; anything else ("A" or
28143 * "a" is recommended) indicates that ob1 and ob2 are azimuth (north
28144 * zero, east 90 deg) and zenith distance. (Zenith distance is used
28145 * rather than altitude in order to reflect the fact that no
28146 * allowance is made for depression of the horizon.)
28147 *
28148 * <li> The accuracy of the result is limited by the corrections for
28149 * refraction, which use a simple A*tan(z) + B*tan^3(z) model.
28150 * Providing the meteorological parameters are known accurately and
28151 * there are no gross local effects, the predicted observed
28152 * coordinates should be within 0.05 arcsec (optical) or 1 arcsec
28153 * (radio) for a zenith distance of less than 70 degrees, better
28154 * than 30 arcsec (optical or radio) at 85 degrees and better than
28155 * 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
28156 *
28157 * <p>Without refraction, the complementary functions iauAtioq and
28158 * iauAtoiq are self-consistent to better than 1 microarcsecond all
28159 * over the celestial sphere. With refraction included, consistency
28160 * falls off at high zenith distances, but is still better than
28161 * 0.05 arcsec at 85 degrees.
28162 *
28163 * <li> It is advisable to take great care with units, as even unlikely
28164 * values of the input parameters are accepted and processed in
28165 * accordance with the models used.
28166 *
28167 * </ol>
28168 * Called:
28169 * <ul>
28170 * <li>{@link #jauS2c} spherical coordinates to unit vector
28171 * <li>{@link #jauC2s} p-vector to spherical
28172 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
28173 *
28174 * </ul>
28175 *@version 2013 October 9
28176 *
28177 *@since JSOFA release 20131202
28178 *
28179 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
28180 */
28181 public static SphericalCoordinate jauAtoiq(String type,
28182 double ob1, double ob2, Astrom astrom
28183 )
28184 {
28185 char c;
28186 double c1, c2, sphi, cphi, ce, xaeo, yaeo, zaeo, v[] = new double[3],
28187 xmhdo, ymhdo, zmhdo, az, sz, zdo, refa, refb, tz, dref,
28188 zdt, xaet, yaet, zaet, xmhda, ymhda, zmhda,
28189 f, xhd, yhd, zhd, xpl, ypl, w;
28190
28191
28192 /* Coordinate type. */
28193 c = type.charAt(0);
28194
28195 /* Coordinates. */
28196 c1 = ob1;
28197 c2 = ob2;
28198
28199 /* Sin, cos of latitude. */
28200 sphi = astrom.sphi;
28201 cphi = astrom.cphi;
28202
28203 /* Standardize coordinate type. */
28204 if ( c == 'r' || c == 'R' ) {
28205 c = 'R';
28206 } else if ( c == 'h' || c == 'H' ) {
28207 c = 'H';
28208 } else {
28209 c = 'A';
28210 }
28211
28212 /* If Az,ZD, convert to Cartesian (S=0,E=90). */
28213 if ( c == 'A' ) {
28214 ce = sin(c2);
28215 xaeo = - cos(c1) * ce;
28216 yaeo = sin(c1) * ce;
28217 zaeo = cos(c2);
28218
28219 } else {
28220
28221 /* If RA,Dec, convert to HA,Dec. */
28222 if ( c == 'R' ) c1 = astrom.eral - c1;
28223
28224 /* To Cartesian -HA,Dec. */
28225 v = jauS2c ( -c1, c2 );
28226 xmhdo = v[0];
28227 ymhdo = v[1];
28228 zmhdo = v[2];
28229
28230 /* To Cartesian Az,El (S=0,E=90). */
28231 xaeo = sphi*xmhdo - cphi*zmhdo;
28232 yaeo = ymhdo;
28233 zaeo = cphi*xmhdo + sphi*zmhdo;
28234 }
28235
28236 /* Azimuth (S=0,E=90). */
28237 az = ( xaeo != 0.0 || yaeo != 0.0 ) ? atan2(yaeo,xaeo) : 0.0;
28238
28239 /* Sine of observed ZD, and observed ZD. */
28240 sz = sqrt ( xaeo*xaeo + yaeo*yaeo );
28241 zdo = atan2 ( sz, zaeo );
28242
28243 /*
28244 * Refraction
28245 * ----------
28246 */
28247
28248 /* Fast algorithm using two constant model. */
28249 refa = astrom.refa;
28250 refb = astrom.refb;
28251 tz = sz / zaeo;
28252 dref = ( refa + refb*tz*tz ) * tz;
28253 zdt = zdo + dref;
28254
28255 /* To Cartesian Az,ZD. */
28256 ce = sin(zdt);
28257 xaet = cos(az) * ce;
28258 yaet = sin(az) * ce;
28259 zaet = cos(zdt);
28260
28261 /* Cartesian Az,ZD to Cartesian -HA,Dec. */
28262 xmhda = sphi*xaet + cphi*zaet;
28263 ymhda = yaet;
28264 zmhda = - cphi*xaet + sphi*zaet;
28265
28266 /* Diurnal aberration. */
28267 f = ( 1.0 + astrom.diurab*ymhda );
28268 xhd = f * xmhda;
28269 yhd = f * ( ymhda - astrom.diurab );
28270 zhd = f * zmhda;
28271
28272 /* Polar motion. */
28273 xpl = astrom.xpl;
28274 ypl = astrom.ypl;
28275 w = xpl*xhd - ypl*yhd + zhd;
28276 v[0] = xhd - xpl*w;
28277 v[1] = yhd + ypl*w;
28278 v[2] = w - ( xpl*xpl + ypl*ypl ) * zhd;
28279
28280 /* To spherical -HA,Dec. */
28281 SphericalCoordinate co = jauC2s(v);
28282
28283 /* Right ascension. */
28284 co.alpha = jauAnp(astrom.eral + co.alpha);
28285
28286 return co;
28287 /* Finished. */
28288
28289
28290 }
28291
28292 /**
28293 * Apply light deflection by a solar-system body, as part of
28294 * transforming coordinate direction into natural direction.
28295 *
28296 *<p>This function is derived from the International Astronomical Union's
28297 * SOFA (Standards of Fundamental Astronomy) software collection.
28298 *
28299 *<p>Status: support function.
28300 *
28301 *<!-- Given: -->
28302 * @param bm double mass of the gravitating body (solar masses)
28303 * @param p double[3] direction from observer to source (unit vector)
28304 * @param q double[3] direction from body to source (unit vector)
28305 * @param e double[3] direction from body to observer (unit vector)
28306 * @param em double distance from body to observer (au)
28307 * @param dlim double deflection limiter (Note 4)
28308 *
28309 *<!-- Returned:-->
28310 * @return p1 double[3] <b>Returned</b> observer to deflected source (unit vector)
28311 *
28312 *<p>Notes:
28313 * <ol>
28314 *
28315 * <li> The algorithm is based on Expr. (70) in Klioner (2003) and
28316 * Expr. (7.63) in the Explanatory Supplement (Urban & Seidelmann
28317 * 2013), with some rearrangement to minimize the effects of machine
28318 * precision.
28319 *
28320 * <li> The mass parameter bm can, as required, be adjusted in order to
28321 * allow for such effects as quadrupole field.
28322 *
28323 * <li> The barycentric position of the deflecting body should ideally
28324 * correspond to the time of closest approach of the light ray to
28325 * the body.
28326 *
28327 * <li> The deflection limiter parameter dlim is phi^2/2, where phi is
28328 * the angular separation (in radians) between source and body at
28329 * which limiting is applied. As phi shrinks below the chosen
28330 * threshold, the deflection is artificially reduced, reaching zero
28331 * for phi = 0.
28332 *
28333 * <li> The returned vector p1 is not normalized, but the consequential
28334 * departure from unit magnitude is always negligible.
28335 *
28336 * <li> The arguments p and p1 can be the same array.
28337 *
28338 * <li> To accumulate total light deflection taking into account the
28339 * contributions from several bodies, call the present function for
28340 * each body in succession, in decreasing order of distance from the
28341 * observer.
28342 *
28343 * <li> For efficiency, validation is omitted. The supplied vectors must
28344 * be of unit magnitude, and the deflection limiter non-zero and
28345 * positive.
28346 *
28347 * </ol>
28348 *<p>References:
28349 * <ul>
28350 *
28351 * <li> Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
28352 * the Astronomical Almanac, 3rd ed., University Science Books
28353 * (2013).
28354 *
28355 * <li> Klioner, Sergei A., "A practical relativistic model for micro-
28356 * arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003).
28357 *
28358 * </ul>
28359 * Called:
28360 * <ul>
28361 * <li>{@link #jauPdp} scalar product of two p-vectors
28362 * <li>{@link #jauPxp} vector product of two p-vectors
28363 *
28364 * </ul>
28365 *@version 2013 October 9
28366 *
28367 *@since JSOFA release 20131202
28368 *
28369 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
28370 */
28371 public static double[] jauLd(double bm, double p[], double q[], double e[],
28372 double em, double dlim)
28373 {
28374 int i;
28375 double qpe[] = new double[3], qdqpe, w, eq[], peq[] ;
28376
28377 double p1[] = new double[3];
28378
28379 /* q . (q + e). */
28380 for (i = 0; i < 3; i++) {
28381 qpe[i] = q[i] + e[i];
28382 }
28383 qdqpe = jauPdp(q, qpe);
28384
28385 /* 2 x G x bm / ( em x c^2 x ( q . (q + e) ) ). */
28386 w = bm * SRS / em / max(qdqpe,dlim);
28387
28388 /* p x (e x q). */
28389 eq = jauPxp(e, q);
28390 peq = jauPxp(p, eq);
28391
28392 /* Apply the deflection. */
28393 for (i = 0; i < 3; i++) {
28394 p1[i] = p[i] + w*peq[i];
28395 }
28396
28397 return p1;
28398 /* Finished. */
28399
28400
28401 }
28402
28403 /*+
28404 * - - - - - - -
28405 * i a u L d n
28406 * - - - - - - -
28407 *
28408 * For a star, apply light deflection by multiple solar-system bodies,
28409 * as part of transforming coordinate direction into natural direction.
28410 *
28411 *<p>This function is derived from the International Astronomical Union's
28412 * SOFA (Standards of Fundamental Astronomy) software collection.
28413 *
28414 *<p>Status: support function.
28415 *
28416 *<!-- Given: -->
28417 * n int number of bodies (note 1)
28418 * b jauLDBODY[n] data for each of the n bodies (Notes 1,2):
28419 * bm double mass of the body (solar masses, Note 3)
28420 * dl double deflection limiter (Note 4)
28421 * pv [2][3] barycentric PV of the body (au, au/day)
28422 * ob double[3] barycentric position of the observer (au)
28423 * sc double[3] observer to star coord direction (unit vector)
28424 *
28425 *<!-- Returned:-->
28426 * sn double[3] observer to deflected star (unit vector)
28427 *
28428 * <li> The array b contains n entries, one for each body to be
28429 * considered. If n = 0, no gravitational light deflection will be
28430 * applied, not even for the Sun.
28431 *
28432 * <li> The array b should include an entry for the Sun as well as for
28433 * any planet or other body to be taken into account. The entries
28434 * should be in the order in which the light passes the body.
28435 *
28436 * <li> In the entry in the b array for body i, the mass parameter
28437 * b[i].bm can, as required, be adjusted in order to allow for such
28438 * effects as quadrupole field.
28439 *
28440 * <li> The deflection limiter parameter b[i].dl is phi^2/2, where phi is
28441 * the angular separation (in radians) between star and body at
28442 * which limiting is applied. As phi shrinks below the chosen
28443 * threshold, the deflection is artificially reduced, reaching zero
28444 * for phi = 0. Example values suitable for a terrestrial
28445 * observer, together with masses, are as follows:
28446 *
28447 * body i b[i].bm b[i].dl
28448 *
28449 * Sun 1.0 6e-6
28450 * Jupiter 0.00095435 3e-9
28451 * Saturn 0.00028574 3e-10
28452 *
28453 * <li> For cases where the starlight passes the body before reaching the
28454 * observer, the body is placed back along its barycentric track by
28455 * the light time from that point to the observer. For cases where
28456 * the body is "behind" the observer no such shift is applied. If
28457 * a different treatment is preferred, the user has the option of
28458 * instead using the iauLd function. Similarly, iauLd can be used
28459 * for cases where the source is nearby, not a star.
28460 *
28461 * <li> The returned vector sn is not normalized, but the consequential
28462 * departure from unit magnitude is always negligible.
28463 *
28464 * <li> The arguments sc and sn can be the same array.
28465 *
28466 * <li> For efficiency, validation is omitted. The supplied masses must
28467 * be greater than zero, the position and velocity vectors must be
28468 * right, and the deflection limiter greater than zero.
28469 *
28470 * Reference:
28471 *
28472 * Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
28473 * the Astronomical Almanac, 3rd ed., University Science Books
28474 * (2013), Section 7.2.4.
28475 *
28476 * Called:
28477 * iauCp copy p-vector
28478 * iauPdp scalar product of two p-vectors
28479 * iauPmp p-vector minus p-vector
28480 * iauPpsp p-vector plus scaled p-vector
28481 * iauPn decompose p-vector into modulus and direction
28482 * iauLd light deflection by a solar-system body
28483 *
28484 *@version 2013 October 9
28485 *
28486 *@since JSOFA release 20131202
28487 *
28488 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
28489 */
28490 public static double[] jauLdn(int n, Ldbody b[], double ob[], double sc[])
28491 {
28492 /* Light time for 1 AU (days) */
28493 final double CR = AULT/DAYSEC;
28494
28495 int i;
28496 double v[] , dt, ev[], sn[] = new double[3];
28497
28498
28499 /* Star direction prior to deflection. */
28500 jauCp(sc, sn);
28501
28502 /* Body by body. */
28503 for ( i = 0; i < n; i++ ) {
28504
28505 /* Body to observer vector at epoch of observation (au). */
28506 v = jauPmp( ob, b[i].pv[0]);
28507
28508 /* Minus the time since the light passed the body (days). */
28509 dt = jauPdp(sn,v) * CR;
28510
28511 /* Neutralize if the star is "behind" the observer. */
28512 dt = min(dt, 0.0);
28513
28514 /* Backtrack the body to the time the light was passing the body. */
28515 ev = jauPpsp(v, -dt, b[i].pv[1]);
28516
28517 /* Body to observer vector as magnitude and direction. */
28518 NormalizedVector nv = jauPn(ev);
28519
28520 /* Apply light deflection for this body. */
28521 sn = jauLd( b[i].bm, sn, sn, nv.u, nv.r, b[i].dl );
28522
28523 /* Next body. */
28524 }
28525 return sn;
28526
28527 /* Finished. */
28528
28529
28530 }
28531
28532 /**
28533 * Deflection of starlight by the Sun.
28534 *
28535 *<p>This function is derived from the International Astronomical Union's
28536 * SOFA (Standards of Fundamental Astronomy) software collection.
28537 *
28538 *<p>Status: support function.
28539 *
28540 *<!-- Given: -->
28541 * @param p double[3] direction from observer to star (unit vector)
28542 * @param e double[3] direction from Sun to observer (unit vector)
28543 * @param em double distance from Sun to observer (au)
28544 *
28545 *<!-- Returned:-->
28546 * @return p1 double[3] <b>Returned</b> observer to deflected start (unit vector)
28547 *
28548 *<p>Notes:
28549 * <ol>
28550 *
28551 * <li> The source is presumed to be sufficiently distant that its
28552 * directions seen from the Sun and the observer are essentially
28553 * the same.
28554 *
28555 * <li> The deflection is restrained when the angle between the star and
28556 * the center of the Sun is less than a threshold value, falling to
28557 * zero deflection for zero separation. The chosen threshold value
28558 * is within the solar limb for all solar-system applications, and
28559 * is about 5 arcminutes for the case of a terrestrial observer.
28560 *
28561 * <li> The arguments p and p1 can be the same array.
28562 *
28563 * </ol>
28564 * Called:
28565 * <ul>
28566 * <li>{@link #jauLd} light deflection by a solar-system body
28567 *
28568 * </ul>
28569 *@version 2016 July 29
28570 *
28571 *@since JSOFA release 20131202
28572 *
28573 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
28574 */
28575 public static double[] jauLdsun(double p[], double e[], double em)
28576 {
28577 double em2, dlim;
28578
28579
28580 /* Deflection limiter (smaller for distant observers). */
28581 em2 = em*em;
28582 if ( em2 < 1.0 ) em2 = 1.0;
28583 dlim = 1e-6 / (em2 > 1.0 ? em2 : 1.0);
28584
28585 /* Apply the deflection. */
28586 return jauLd(1.0, p, p, e, em, dlim);
28587
28588 }
28589
28590 /**
28591 * Proper motion and parallax.
28592 *
28593 *<p>This function is derived from the International Astronomical Union's
28594 * SOFA (Standards of Fundamental Astronomy) software collection.
28595 *
28596 *<p>Status: support function.
28597 *
28598 *<!-- Given: -->
28599 * @param rc double ICRS RA,Dec at catalog epoch (radians)
28600 * @param dc double ICRS RA,Dec at catalog epoch (radians)
28601 * @param pr double RA proper motion (radians/year; Note 1)
28602 * @param pd double Dec proper motion (radians/year)
28603 * @param px double parallax (arcsec)
28604 * @param rv double radial velocity (km/s, +ve if receding)
28605 * @param pmt double proper motion time interval (SSB, Julian years)
28606 * @param pob double[3] SSB to observer vector (au)
28607 *
28608 *<!-- Returned:-->
28609 * @return pco double[3] <b>Returned</b> coordinate direction (BCRS unit vector)
28610 *
28611 *<p>Notes:
28612 * <ol>
28613 *
28614 * <li> The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
28615 *
28616 * <li> The proper motion time interval is for when the starlight
28617 * reaches the solar system barycenter.
28618 *
28619 * <li> To avoid the need for iteration, the Roemer effect (i.e. the
28620 * small annual modulation of the proper motion coming from the
28621 * changing light time) is applied approximately, using the
28622 * direction of the star at the catalog epoch.
28623 *
28624 * </ol>
28625 *<p>References:
28626 * <ul>
28627 *
28628 * <li> 1984 Astronomical Almanac, pp B39-B41.
28629 *
28630 * <li> Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
28631 * the Astronomical Almanac, 3rd ed., University Science Books
28632 * (2013), Section 7.2.
28633 *
28634 * </ul>
28635 * Called:
28636 * <ul>
28637 * <li>{@link #jauPdp} scalar product of two p-vectors
28638 * <li>{@link #jauPn} decompose p-vector into modulus and direction
28639 *
28640 * </ul>
28641 *@version 2013 October 9
28642 *
28643 *@since JSOFA release 20131202
28644 *
28645 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
28646 */
28647 public static double[] jauPmpx(double rc, double dc, double pr, double pd,
28648 double px, double rv, double pmt, double pob[]
28649 )
28650 {
28651 /* Km/s to au/year */
28652 final double VF = DAYSEC*DJM/DAU;
28653
28654 /* Light time for 1 au, Julian years */
28655 final double AULTY = AULT/DAYSEC/DJY;
28656
28657 int i;
28658 double sr, cr, sd, cd, x, y, z, p[] = new double[3], dt, pxr, w, pdz, pm[] = new double[3];
28659
28660
28661 /* Spherical coordinates to unit vector (and useful functions). */
28662 sr = sin(rc);
28663 cr = cos(rc);
28664 sd = sin(dc);
28665 cd = cos(dc);
28666 p[0] = x = cr*cd;
28667 p[1] = y = sr*cd;
28668 p[2] = z = sd;
28669
28670 /* Proper motion time interval (y) including Roemer effect. */
28671 dt = pmt + jauPdp(p,pob)*AULTY;
28672
28673 /* Space motion (radians per year). */
28674 pxr = px * DAS2R;
28675 w = VF * rv * pxr;
28676 pdz = pd * z;
28677 pm[0] = - pr*y - pdz*cr + w*x;
28678 pm[1] = pr*x - pdz*sr + w*y;
28679 pm[2] = pd*cd + w*z;
28680
28681 /* Coordinate direction of star (unit vector, BCRS). */
28682 for (i = 0; i < 3; i++) {
28683 p[i] += dt*pm[i] - pxr*pob[i];
28684 }
28685 NormalizedVector pco = jauPn(p);
28686
28687 return pco.u;
28688 /* Finished. */
28689
28690
28691 }
28692
28693 /**
28694 * Star proper motion: update star catalog data for space motion, with
28695 * special handling to handle the zero parallax case.
28696 *
28697 *<p>This function is derived from the International Astronomical Union's
28698 * SOFA (Standards of Fundamental Astronomy) software collection.
28699 *
28700 *<p>Status: support function.
28701 *
28702 *<!-- Given: -->
28703 * @param ra1 double right ascension (radians), before
28704 * @param dec1 double declination (radians), before
28705 * @param pmr1 double RA proper motion (radians/year), before
28706 * @param pmd1 double Dec proper motion (radians/year), before
28707 * @param px1 double parallax (arcseconds), before
28708 * @param rv1 double radial velocity (km/s, +ve = receding), before
28709 * @param ep1a double "before" epoch, part A (Note 1)
28710 * @param ep1b double "before" epoch, part B (Note 1)
28711 * @param ep2a double "after" epoch, part A (Note 1)
28712 * @param ep2b double "after" epoch, part B (Note 1)
28713 *
28714 *<!-- Returned:-->
28715 * @return ra2 double <b>Returned</b> right ascension (radians), after
28716 * dec2 double <b>Returned</b> declination (radians), after
28717 * pmr2 double <b>Returned</b> RA proper motion (radians/year), after
28718 * pmd2 double <b>Returned</b> Dec proper motion (radians/year), after
28719 * px2 double <b>Returned</b> parallax (arcseconds), after
28720 * rv2 double <b>Returned</b> radial velocity (km/s, +ve = receding), after
28721 *
28722 * @throws JSOFAInternalError
28723 * int status:
28724 * -1 = <b>Returned</b> system error (should not occur)
28725 * 0 = <b>Returned</b> no warnings or errors
28726 * 1 = <b>Returned</b> distance overridden (Note 6)
28727 * 2 = <b>Returned</b> excessive velocity (Note 7)
28728 * 4 = <b>Returned</b> solution didn't converge (Note 8)
28729 * else = <b>Returned</b> binary logical OR of the above warnings
28730 *
28731 *<p>Notes:
28732 * <ol>
28733 *
28734 * <li> The starting and ending TDB epochs ep1a+ep1b and ep2a+ep2b are
28735 * Julian Dates, apportioned in any convenient way between the two
28736 * parts (A and B). For example, JD(TDB)=2450123.7 could be
28737 * expressed in any of these ways, among others:
28738 *
28739 * <p>epNa epNb
28740 *
28741 * 2450123.7 0.0 (JD method)
28742 * 2451545.0 -1421.3 (J2000 method)
28743 * 2400000.5 50123.2 (MJD method)
28744 * 2450123.5 0.2 (date & time method)
28745 *
28746 * <p>The JD method is the most natural and convenient to use in cases
28747 * where the loss of several decimal digits of resolution is
28748 * acceptable. The J2000 method is best matched to the way the
28749 * argument is handled internally and will deliver the optimum
28750 * resolution. The MJD method and the date & time methods are both
28751 * good compromises between resolution and convenience.
28752 *
28753 * <li> In accordance with normal star-catalog conventions, the object's
28754 * right ascension and declination are freed from the effects of
28755 * secular aberration. The frame, which is aligned to the catalog
28756 * equator and equinox, is Lorentzian and centered on the SSB.
28757 *
28758 * <p>The proper motions are the rate of change of the right ascension
28759 * and declination at the catalog epoch and are in radians per TDB
28760 * Julian year.
28761 *
28762 * <p>The parallax and radial velocity are in the same frame.
28763 *
28764 * <li> Care is needed with units. The star coordinates are in radians
28765 * and the proper motions in radians per Julian year, but the
28766 * parallax is in arcseconds.
28767 *
28768 * <li> The RA proper motion is in terms of coordinate angle, not true
28769 * angle. If the catalog uses arcseconds for both RA and Dec proper
28770 * motions, the RA proper motion will need to be divided by cos(Dec)
28771 * before use.
28772 *
28773 * <li> Straight-line motion at constant speed, in the inertial frame, is
28774 * assumed.
28775 *
28776 * <li> An extremely small (or zero or negative) parallax is overridden
28777 * to ensure that the object is at a finite but very large distance,
28778 * but not so large that the proper motion is equivalent to a large
28779 * but safe speed (about 0.1c using the chosen constant). A warning
28780 * status of 1 is added to the status if this action has been taken.
28781 *
28782 * <li> If the space velocity is a significant fraction of c (see the
28783 * constant VMAX in the function iauStarpv), it is arbitrarily set
28784 * to zero. When this action occurs, 2 is added to the status.
28785 *
28786 * <li> The relativistic adjustment carried out in the iauStarpv function
28787 * involves an iterative calculation. If the process fails to
28788 * converge within a set number of iterations, 4 is added to the
28789 * status.
28790 *
28791 * </ol>
28792 * Called:
28793 * <ul>
28794 * <li>{@link #jauSeps} angle between two points
28795 * <li>{@link #jauStarpm} update star catalog data for space motion
28796 *
28797 * </ul>
28798 *@version 2013 October 9
28799 *
28800 *@since JSOFA release 20131202
28801 *
28802 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
28803 * @throws JSOFAInternalError
28804 */
28805 public static CatalogCoords jauPmsafe(double ra1, double dec1, double pmr1, double pmd1,
28806 double px1, double rv1,
28807 double ep1a, double ep1b, double ep2a, double ep2b) throws JSOFAInternalError
28808 {
28809
28810 /* Minimum allowed parallax (arcsec) */
28811 final double PXMIN = 5e-7;
28812
28813 /* Factor giving maximum allowed transverse speed of about 1% c */
28814 final double F = 326.0;
28815
28816 double pm, px1a;
28817
28818
28819 /* Proper motion in one year (radians). */
28820 pm = jauSeps(ra1, dec1, ra1+pmr1, dec1+pmd1);
28821
28822
28823 px1a = px1;
28824 pm *= F;
28825 if (px1a < pm) {px1a = pm;}
28826 if (px1a < PXMIN) {px1a = PXMIN;}
28827
28828 /* Carry out the transformation using the modified parallax. */
28829 return jauStarpm(ra1, dec1, pmr1, pmd1, px1a, rv1,
28830 ep1a, ep1b, ep2a, ep2b);
28831
28832 /* Finished. */
28833
28834
28835 }
28836
28837 /**
28838 * Position and velocity of a terrestrial observing station.
28839 *
28840 *<p>This function is derived from the International Astronomical Union's
28841 * SOFA (Standards of Fundamental Astronomy) software collection.
28842 *
28843 *<p>Status: support function.
28844 *
28845 *<!-- Given: -->
28846 * @param elong double longitude (radians, east +ve, Note 1)
28847 * @param phi double latitude (geodetic, radians, Note 1)
28848 * @param hm double height above ref. ellipsoid (geodetic, m)
28849 * @param xp double coordinates of the pole (radians, Note 2)
28850 * @param yp double coordinates of the pole (radians, Note 2)
28851 * @param sp double the TIO locator s' (radians, Note 2)
28852 * @param theta double Earth rotation angle (radians, Note 3)
28853 *
28854 *<!-- Returned:-->
28855 * @return pv double[2][3] <b>Returned</b> position/velocity vector (m, m/s, CIRS)
28856 *
28857 *<p>Notes:
28858 * <ol>
28859 *
28860 * <li> The terrestrial coordinates are with respect to the WGS84
28861 * reference ellipsoid.
28862 *
28863 * <li> xp and yp are the coordinates (in radians) of the Celestial
28864 * Intermediate Pole with respect to the International Terrestrial
28865 * Reference System (see IERS Conventions), measured along the
28866 * meridians 0 and 90 deg west respectively. sp is the TIO locator
28867 * s', in radians, which positions the Terrestrial Intermediate
28868 * Origin on the equator. For many applications, xp, yp and
28869 * (especially) sp can be set to zero.
28870 *
28871 * <li> If theta is Greenwich apparent sidereal time instead of Earth
28872 * rotation angle, the result is with respect to the true equator
28873 * and equinox of date, i.e. with the x-axis at the equinox rather
28874 * than the celestial intermediate origin.
28875 *
28876 * <li> The velocity units are meters per UT1 second, not per SI second.
28877 * This is unlikely to have any practical consequences in the modern
28878 * era.
28879 *
28880 * <li> No validation is performed on the arguments. Error cases that
28881 * could lead to arithmetic exceptions are trapped by the iauGd2gc
28882 * function, and the result set to zeros.
28883 *
28884 * </ol>
28885 *<p>References:
28886 * <ul>
28887 *
28888 * <li> McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
28889 * IERS Technical Note No. 32, BKG (2004)
28890 *
28891 * <li> Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
28892 * the Astronomical Almanac, 3rd ed., University Science Books
28893 * (2013), Section 7.4.3.3.
28894 *
28895 * </ul>
28896 * Called:
28897 * <ul>
28898 * <li>{@link #jauGd2gc} geodetic to geocentric transformation
28899 * <li>{@link #jauPom00} polar motion matrix
28900 * <li>{@link #jauTrxp} product of transpose of r-matrix and p-vector
28901 *
28902 * </ul>
28903 *@version 2013 October 9
28904 *
28905 * @since JSOFA release 20131202
28906 *
28907 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
28908 * @throws JSOFAInternalError
28909 * @throws JSOFAIllegalParameter
28910 */
28911 public static double [][] jauPvtob(double elong, double phi, double hm,
28912 double xp, double yp, double sp, double theta
28913 ) throws JSOFAIllegalParameter, JSOFAInternalError
28914 {
28915
28916 double xyzm[];
28917
28918 /* Geodetic to geocentric transformation (WGS84). */
28919 xyzm = jauGd2gc(1, elong, phi, hm);
28920
28921 return jauPvtob(xyzm, xp, yp, sp, theta );
28922 /* Finished. */
28923
28924
28925 }
28926
28927 /**
28928 * Alternative Position and velocity of a terrestrial observing station with observatory position already in cartesian.
28929 * @see JSOFA#jauPvtob(double, double, double, double, double, double, double) for more detail.
28930 * @param xyzm observatory geocentric position in metres.
28931 * @param xp double coordinates of the pole (radians, Note 2)
28932 * @param yp double coordinates of the pole (radians, Note 2)
28933 * @param sp double the TIO locator s' (radians, Note 2)
28934 * @param theta double Earth rotation angle (radians, Note 3)
28935 * @return pv double[2][3] <b>Returned</b> position/velocity vector (m, m/s, CIRS)
28936 * @throws JSOFAIllegalParameter
28937 * @throws JSOFAInternalError
28938 */
28939 public static double [][] jauPvtob(double xyzm[],
28940 double xp, double yp, double sp, double theta
28941 ) throws JSOFAIllegalParameter, JSOFAInternalError
28942 {
28943 /* Earth rotation rate in radians per UT1 second */
28944 final double OM = 1.00273781191135448 * D2PI / DAYSEC;
28945
28946 double rpm[][], xyz[], x, y, z, s, c;
28947 double pv[][] = new double[2][3];
28948
28949
28950 /* Polar motion and TIO position. */
28951 rpm = jauPom00(xp, yp, sp);
28952 xyz = jauTrxp(rpm, xyzm);
28953 x = xyz[0];
28954 y = xyz[1];
28955 z = xyz[2];
28956
28957 /* Functions of ERA. */
28958 s = sin(theta);
28959 c = cos(theta);
28960
28961 /* Position. */
28962 pv[0][0] = c*x - s*y;
28963 pv[0][1] = s*x + c*y;
28964 pv[0][2] = z;
28965
28966 /* Velocity. */
28967 pv[1][0] = OM * ( -s*x - c*y );
28968 pv[1][1] = OM * ( c*x - s*y );
28969 pv[1][2] = 0.0;
28970
28971 return pv;
28972 /* Finished. */
28973
28974
28975 }
28976
28977 /**
28978 * constants A and B in the atmospheric refraction model
28979 * dZ = A tan Z + B tan^3 Z.
28980 * .
28981 * @author Paul Harrison (paul.harrison@manchester.ac.uk) 28 Mar 2014
28982 * @version $Revision$ $date$
28983 */
28984 public static class RefCos {
28985 /** refraction coefficient A */
28986 public double a ;
28987
28988 /** refraction coefficient B */
28989 public double b ;
28990 public RefCos(double a, double b) {
28991 this.a = a;
28992 this.b = b;
28993 }
28994
28995 }
28996
28997 /**
28998 * Determine the constants A and B in the atmospheric refraction model
28999 * dZ = A tan Z + B tan^3 Z.
29000 *
29001 * Z is the "observed" zenith distance (i.e. affected by refraction)
29002 * and dZ is what to add to Z to give the "topocentric" (i.e. in vacuo)
29003 * zenith distance.
29004 *
29005 *<p>This function is derived from the International Astronomical Union's
29006 * SOFA (Standards of Fundamental Astronomy) software collection.
29007 *
29008 *<p>Status: support function.
29009 *
29010 *<!-- Given: -->
29011 * @param phpa double pressure at the observer (hPa = millibar)
29012 * @param tc double ambient temperature at the observer (deg C)
29013 * @param rh double relative humidity at the observer (range 0-1)
29014 * @param wl double wavelength (micrometers)
29015 *
29016 *<!-- Returned:-->
29017 * @return <b>Returned</b> tan Z coefficient (radians)
29018 * <b>Returned</b> tan^3 Z coefficient (radians)
29019 *
29020 *<p>Notes:
29021 * <ol>
29022 *
29023 * <li> The model balances speed and accuracy to give good results in
29024 * applications where performance at low altitudes is not paramount.
29025 * Performance is maintained across a range of conditions, and
29026 * applies to both optical/IR and radio.
29027 *
29028 * <li> The model omits the effects of (i) height above sea level (apart
29029 * from the reduced pressure itself), (ii) latitude (i.e. the
29030 * flattening of the Earth), (iii) variations in tropospheric lapse
29031 * rate and (iv) dispersive effects in the radio.
29032 *
29033 * <p>The model was tested using the following range of conditions:
29034 *
29035 * <p>lapse rates 0.0055, 0.0065, 0.0075 deg/meter
29036 * latitudes 0, 25, 50, 75 degrees
29037 * heights 0, 2500, 5000 meters ASL
29038 * pressures mean for height -10% to +5% in steps of 5%
29039 * temperatures -10 deg to +20 deg with respect to 280 deg at SL
29040 * relative humidity 0, 0.5, 1
29041 * wavelengths 0.4, 0.6, ... 2 micron, + radio
29042 * zenith distances 15, 45, 75 degrees
29043 *
29044 * <p>The accuracy with respect to raytracing through a model
29045 * atmosphere was as follows:
29046 *
29047 * <p>worst RMS
29048 *
29049 * <p>optical/IR 62 mas 8 mas
29050 * radio 319 mas 49 mas
29051 *
29052 * <p>For this particular set of conditions:
29053 *
29054 * <p>lapse rate 0.0065 K/meter
29055 * latitude 50 degrees
29056 * sea level
29057 * pressure 1005 mb
29058 * temperature 280.15 K
29059 * humidity 80%
29060 * wavelength 5740 Angstroms
29061 *
29062 * <p>the results were as follows:
29063 *
29064 * <p>ZD raytrace iauRefco Saastamoinen
29065 *
29066 * 10 10.27 10.27 10.27
29067 * 20 21.19 21.20 21.19
29068 * 30 33.61 33.61 33.60
29069 * 40 48.82 48.83 48.81
29070 * 45 58.16 58.18 58.16
29071 * 50 69.28 69.30 69.27
29072 * 55 82.97 82.99 82.95
29073 * 60 100.51 100.54 100.50
29074 * 65 124.23 124.26 124.20
29075 * 70 158.63 158.68 158.61
29076 * 72 177.32 177.37 177.31
29077 * 74 200.35 200.38 200.32
29078 * 76 229.45 229.43 229.42
29079 * 78 267.44 267.29 267.41
29080 * 80 319.13 318.55 319.10
29081 *
29082 * <p>deg arcsec arcsec arcsec
29083 *
29084 * <p>The values for Saastamoinen's formula (which includes terms
29085 * up to tan^5) are taken from Hohenkerk and Sinclair (1985).
29086 *
29087 * <li> A wl value in the range 0-100 selects the optical/IR case and is
29088 * wavelength in micrometers. Any value outside this range selects
29089 * the radio case.
29090 *
29091 * <li> Outlandish input parameters are silently limited to
29092 * mathematically safe values. Zero pressure is permissible, and
29093 * causes zeroes to be returned.
29094 *
29095 * <li> The algorithm draws on several sources, as follows:
29096 *
29097 * <p>a) The formula for the saturation vapour pressure of water as
29098 * a function of temperature and temperature is taken from
29099 * Equations (A4.5-A4.7) of Gill (1982).
29100 *
29101 * <p>b) The formula for the water vapour pressure, given the
29102 * saturation pressure and the relative humidity, is from
29103 * Crane (1976), Equation (2.5.5).
29104 *
29105 * <p>c) The refractivity of air is a function of temperature,
29106 * total pressure, water-vapour pressure and, in the case
29107 * of optical/IR, wavelength. The formulae for the two cases are
29108 * developed from Hohenkerk & Sinclair (1985) and Rueger (2002).
29109 *
29110 * <p>d) The formula for beta, the ratio of the scale height of the
29111 * atmosphere to the geocentric distance of the observer, is
29112 * an adaption of Equation (9) from Stone (1996). The
29113 * adaptations, arrived at empirically, consist of (i) a small
29114 * adjustment to the coefficient and (ii) a humidity term for the
29115 * radio case only.
29116 *
29117 * <p>e) The formulae for the refraction constants as a function of
29118 * n-1 and beta are from Green (1987), Equation (4.31).
29119 *
29120 * </ol>
29121 *<p>References:
29122 * <ul>
29123 *
29124 * <li> Crane, R.K., Meeks, M.L. (ed), "Refraction Effects in the Neutral
29125 * Atmosphere", Methods of Experimental Physics: Astrophysics 12B,
29126 * Academic Press, 1976.
29127 *
29128 * <li> Gill, Adrian E., "Atmosphere-Ocean Dynamics", Academic Press,
29129 * 1982.
29130 *
29131 * <li> Green, R.M., "Spherical Astronomy", Cambridge University Press,
29132 * 1987.
29133 *
29134 * <li> Hohenkerk, C.Y., & Sinclair, A.T., NAO Technical Note No. 63,
29135 * 1985.
29136 *
29137 * <li> Rueger, J.M., "Refractive Index Formulae for Electronic Distance
29138 * Measurement with Radio and Millimetre Waves", in Unisurv Report
29139 * S-68, School of Surveying and Spatial Information Systems,
29140 * University of New South Wales, Sydney, Australia, 2002.
29141 *
29142 * <li> Stone, Ronald C., P.A.S.P. 108, 1051-1058, 1996.
29143 *
29144 * </ul>
29145 *@version 2013 October 9
29146 *
29147 *@since JSOFA release 20131202
29148 *
29149 * <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
29150 */
29151 public static RefCos jauRefco(double phpa, double tc, double rh, double wl )
29152 {
29153 boolean optic;
29154 double p, t, r, w, ps, pw, tk, wlsq, gamma, beta;
29155
29156
29157 /* Decide whether optical/IR or radio case: switch at 100 microns. */
29158 optic = ( wl <= 100.0 );
29159
29160 /* Restrict parameters to safe values. */
29161 t = max ( tc, -150.0 );
29162 t = min ( t, 200.0 );
29163 p = max ( phpa, 0.0 );
29164 p = min ( p, 10000.0 );
29165 r = max ( rh, 0.0 );
29166 r = min ( r, 1.0 );
29167 w = max ( wl, 0.1 );
29168 w = min ( w, 1e6 );
29169
29170 /* Water vapour pressure at the observer. */
29171 if ( p > 0.0 ) {
29172 ps = pow ( 10.0, ( 0.7859 + 0.03477*t ) /
29173 ( 1.0 + 0.00412*t ) ) *
29174 ( 1.0 + p * ( 4.5e-6 + 6e-10*t*t ) );
29175 pw = r * ps / ( 1.0 - (1.0-r)*ps/p );
29176 } else {
29177 pw = 0.0;
29178 }
29179
29180 /* Refractive index minus 1 at the observer. */
29181 tk = t + 273.15;
29182 if ( optic ) {
29183 wlsq = w * w;
29184 gamma = ( ( 77.53484e-6 +
29185 ( 4.39108e-7 + 3.666e-9/wlsq ) / wlsq ) * p
29186 - 11.2684e-6*pw ) / tk;
29187 } else {
29188 gamma = ( 77.6890e-6*p - ( 6.3938e-6 - 0.375463/tk ) * pw ) / tk;
29189 }
29190
29191 /* Formula for beta from Stone, with empirical adjustments. */
29192 beta = 4.4474e-6 * tk;
29193 if ( ! optic ) beta -= 0.0074 * pw * beta;
29194
29195 /* Refraction constants from Green. */
29196 return new RefCos( gamma * ( 1.0 - beta ),
29197 - gamma * ( beta - gamma / 2.0 ));
29198
29199 /* Finished. */
29200
29201
29202 }
29203
29204
29205 /**
29206 * Transformation from Galactic Coordinates to ICRS.
29207 *
29208 * This function is derived from the International Astronomical Union's
29209 * SOFA (Standards of Fundamental Astronomy) software collection.
29210 *
29211 * <p>Status: support routine.
29212 *
29213 * @param dl double galactic longitude (radians)
29214 * @param db double galactic latitude (radians)
29215 *
29216 * @return co ICRS right ascension, declination.
29217 *
29218 * <p>Notes:<ol>
29219 *
29220 * <li> The IAU 1958 system of Galactic coordinates was defined with
29221 * respect to the now obsolete reference system FK4 B1950.0. When
29222 * interpreting the system in a modern context, several factors have
29223 * to be taken into account:<ul>
29224 *
29225 * <li> The inclusion in FK4 positions of the E-terms of aberration.
29226 *
29227 * <li> The distortion of the FK4 proper motion system by differential
29228 * Galactic rotation.
29229 *
29230 * <li> The use of the B1950.0 equinox rather than the now-standard
29231 * J2000.0.
29232 *
29233 * <li> The frame bias between ICRS and the J2000.0 mean place system.
29234 * </ul>
29235 * The Hipparcos Catalogue (Perryman & ESA 1997) provides a rotation
29236 * matrix that transforms directly between ICRS and Galactic
29237 * coordinates with the above factors taken into account. The
29238 * matrix is derived from three angles, namely the ICRS coordinates
29239 * of the Galactic pole and the longitude of the ascending node of
29240 * the galactic equator on the ICRS equator. They are given in
29241 * degrees to five decimal places and for canonical purposes are
29242 * regarded as exact. In the Hipparcos Catalogue the matrix
29243 * elements are given to 10 decimal places (about 20 microarcsec).
29244 * In the present SOFA function the matrix elements have been
29245 * recomputed from the canonical three angles and are given to 30
29246 * decimal places.
29247 *
29248 * <li> The inverse transformation is performed by the function jauIcrs2g.
29249 * </ol>
29250 *
29251 * Reference:
29252 * Perryman M.A.C. & ESA, 1997, ESA SP-1200, The Hipparcos and Tycho
29253 * catalogues. Astrometric and photometric star catalogues
29254 * derived from the ESA Hipparcos Space Astrometry Mission. ESA
29255 * Publications Division, Noordwijk, Netherlands.
29256 *
29257 * @version 2015 March 02
29258 *
29259 *
29260 * @since JSOFA release 20150209
29261 *
29262 */
29263 public static SphericalCoordinate jauG2icrs ( double dl, double db)
29264 {
29265 double v1[], v2[];
29266
29267 /*
29268 * L2,B2 system of galactic coordinates in the form presented in the
29269 * Hipparcos Catalogue. In degrees:
29270 *
29271 * P = 192.85948 right ascension of the Galactic north pole in ICRS
29272 * Q = 27.12825 declination of the Galactic north pole in ICRS
29273 * R = 32.93192 longitude of the ascending node of the Galactic
29274 * plane on the ICRS equator
29275 *
29276 * ICRS to galactic rotation matrix, obtained by computing
29277 * R_3(-R) R_1(pi/2-Q) R_3(pi/2+P) to the full precision shown:
29278 */
29279 double r[][] = new double[][]{ { -0.054875560416215368492398900454,
29280 -0.873437090234885048760383168409,
29281 -0.483835015548713226831774175116 },
29282 { +0.494109427875583673525222371358,
29283 -0.444829629960011178146614061616,
29284 +0.746982244497218890527388004556 },
29285 { -0.867666149019004701181616534570,
29286 -0.198076373431201528180486091412,
29287 +0.455983776175066922272100478348 } };
29288
29289
29290 /* Spherical to Cartesian. */
29291 v1 = jauS2c(dl, db);
29292
29293 /* Galactic to ICRS. */
29294 v2 = jauTrxp(r, v1);
29295
29296 /* Cartesian to spherical. */
29297 SphericalCoordinate co = jauC2s(v2);
29298
29299 /* Express in conventional ranges. */
29300 co.alpha = jauAnp(co.alpha);
29301 co.delta = jauAnpm(co.delta);
29302
29303 /* Finished. */
29304 return co;
29305 }
29306
29307
29308
29309 /**
29310 * Transformation from ICRS to Galactic Coordinates.
29311 *
29312 * This function is derived from the International Astronomical Union's
29313 * SOFA (Standards of Fundamental Astronomy) software collection.
29314 *
29315 * <p>Status: support routine.
29316 *
29317 * @param dr double ICRS right ascension (radians)
29318 * @param dd double ICRS declination (radians)
29319 *
29320 * @return co galactic longitude (radians), galactic latitude (radians)
29321 *
29322 * <p>Notes:<ol>
29323 *
29324 * <li> The IAU 1958 system of Galactic coordinates was defined with
29325 * respect to the now obsolete reference system FK4 B1950.0. When
29326 * interpreting the system in a modern context, several factors have
29327 * to be taken into account:<ul>
29328 *
29329 * <li> The inclusion in FK4 positions of the E-terms of aberration.
29330 *
29331 * <li> The distortion of the FK4 proper motion system by differential
29332 * Galactic rotation.
29333 *
29334 * <li> The use of the B1950.0 equinox rather than the now-standard
29335 * J2000.0.
29336 *
29337 * <li> The frame bias between ICRS and the J2000.0 mean place system.
29338 * </ul>
29339 * The Hipparcos Catalogue (Perryman & ESA 1997) provides a rotation
29340 * matrix that transforms directly between ICRS and Galactic
29341 * coordinates with the above factors taken into account. The
29342 * matrix is derived from three angles, namely the ICRS coordinates
29343 * of the Galactic pole and the longitude of the ascending node of
29344 * the galactic equator on the ICRS equator. They are given in
29345 * degrees to five decimal places and for canonical purposes are
29346 * regarded as exact. In the Hipparcos Catalogue the matrix
29347 * elements are given to 10 decimal places (about 20 microarcsec).
29348 * In the present SOFA function the matrix elements have been
29349 * recomputed from the canonical three angles and are given to 30
29350 * decimal places.
29351 *
29352 * <li> The inverse transformation is performed by the function iauG2icrs.
29353 * </ol>
29354 * Reference:
29355 * Perryman M.A.C. & ESA, 1997, ESA SP-1200, The Hipparcos and Tycho
29356 * catalogues. Astrometric and photometric star catalogues
29357 * derived from the ESA Hipparcos Space Astrometry Mission. ESA
29358 * Publications Division, Noordwijk, Netherlands.
29359 *
29360 * @version 2015 January 20
29361 *
29362 * @since JSOFA release 20150209
29363 *
29364 */
29365 public static SphericalCoordinate jauIcrs2g ( double dr, double dd )
29366 {
29367 double v1[], v2[];
29368
29369 /*
29370 * L2,B2 system of galactic coordinates in the form presented in the
29371 * Hipparcos Catalogue. In degrees:
29372 *
29373 * P = 192.85948 right ascension of the Galactic north pole in ICRS
29374 * Q = 27.12825 declination of the Galactic north pole in ICRS
29375 * R = 32.93192 longitude of the ascending node of the Galactic
29376 * plane on the ICRS equator
29377 *
29378 * ICRS to galactic rotation matrix, obtained by computing
29379 * R_3(-R) R_1(pi/2-Q) R_3(pi/2+P) to the full precision shown:
29380 */
29381 double r[][] = new double[][] { { -0.054875560416215368492398900454,
29382 -0.873437090234885048760383168409,
29383 -0.483835015548713226831774175116 },
29384 { +0.494109427875583673525222371358,
29385 -0.444829629960011178146614061616,
29386 +0.746982244497218890527388004556 },
29387 { -0.867666149019004701181616534570,
29388 -0.198076373431201528180486091412,
29389 +0.455983776175066922272100478348 } };
29390
29391
29392 /* Spherical to Cartesian. */
29393 v1 = jauS2c(dr, dd);
29394
29395 /* ICRS to Galactic. */
29396 v2 = jauRxp(r, v1);
29397
29398 /* Cartesian to spherical. */
29399 SphericalCoordinate co = jauC2s(v2);
29400
29401 /* Express in conventional ranges. */
29402 co.alpha = jauAnp(co.alpha);
29403 co.delta = jauAnpm(co.delta);
29404 return co;
29405 }
29406
29407 // 2016-05-03 additions below
29408
29409 /**
29410 *
29411 * Transformation from ecliptic coordinates (mean equinox and ecliptic
29412 * of date) to ICRS RA,Dec, using the IAU 2006 precession model.
29413 *
29414 * <p>This function is derived from the International Astronomical Union's
29415 * SOFA (Standards of Fundamental Astronomy) software collection.
29416 *
29417 * <p>Status: support function.
29418 *
29419 * <!-- Given: -->
29420 * @param date1 double TT as a 2-part Julian date (Note 1)
29421 * @param date2 double TT as a 2-part Julian date (Note 1)
29422 * @param dl double ecliptic longitude and latitude (radians)
29423 * @param db double ecliptic longitude and latitude (radians)
29424 *
29425 * <!-- Returned: -->
29426 * @return double ICRS right ascension and declination (radians)
29427 *
29428 *<ol>
29429 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
29430 * convenient way between the two arguments. For example,
29431 * JD(TT)=2450123.7 could be expressed in any of these ways,
29432 * among others:
29433 *
29434 * date1 date2
29435 *
29436 * 2450123.7 0.0 (JD method)
29437 * 2451545.0 -1421.3 (J2000 method)
29438 * 2400000.5 50123.2 (MJD method)
29439 * 2450123.5 0.2 (date & time method)
29440 *
29441 * The JD method is the most natural and convenient to use in
29442 * cases where the loss of several decimal digits of resolution
29443 * is acceptable. The J2000 method is best matched to the way
29444 * the argument is handled internally and will deliver the
29445 * optimum resolution. The MJD method and the date & time methods
29446 * are both good compromises between resolution and convenience.
29447 *
29448 * <li> No assumptions are made about whether the coordinates represent
29449 * starlight and embody astrometric effects such as parallax or
29450 * aberration.
29451 *
29452 * <li> The transformation is approximately that from ecliptic longitude
29453 * and latitude (mean equinox and ecliptic of date) to mean J2000.0
29454 * right ascension and declination, with only frame bias (always
29455 * less than 25 mas) to disturb this classical picture.
29456 *</ol>
29457 * Called: <ul>
29458 * <li>{@link #jauS2c} spherical coordinates to unit vector
29459 * <li>{@link #jauEcm06} J2000.0 to ecliptic rotation matrix, IAU 2006
29460 * <li>{@link #jauTrxp} product of transpose of r-matrix and p-vector
29461 * <li>{@link #jauC2s} unit vector to spherical coordinates
29462 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
29463 * <li>{@link #jauAnpm} normalize angle into range +/- pi
29464 *</ul>
29465 *
29466 * @version 2016 February 9
29467 *
29468 * @since JSOFA release 20160503
29469 *
29470 * <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
29471 */
29472 public static SphericalCoordinate jauEceq06(double date1, double date2, double dl, double db)
29473 {
29474
29475
29476 /* Spherical to Cartesian. */
29477 double v1[] = jauS2c(dl, db);
29478
29479 /* Rotation matrix, ICRS equatorial to ecliptic. */
29480 double rm[][] = jauEcm06(date1, date2);
29481
29482 /* The transformation from ecliptic to ICRS. */
29483 double v2[] = jauTrxp(rm, v1);
29484
29485 /* Cartesian to spherical. */
29486 SphericalCoordinate co = jauC2s(v2);
29487
29488 /* Express in conventional ranges. */
29489 co.alpha = jauAnp(co.alpha);
29490 co.delta = jauAnpm(co.delta);
29491
29492 return co;
29493 }
29494
29495 /**
29496 *
29497 * ICRS equatorial to ecliptic rotation matrix, IAU 2006.
29498 *
29499 * <p>This function is derived from the International Astronomical Union's
29500 * SOFA (Standards of Fundamental Astronomy) software collection.
29501 *
29502 * <p>Status: support function.
29503 *
29504 * <!-- Given: -->
29505 * @param date1 double TT as a 2-part Julian date (Note 1)
29506 * @param date2 double TT as a 2-part Julian date (Note 1)
29507 *
29508 * <!-- Returned: -->
29509 * @return double[3][3] ICRS to ecliptic rotation matrix
29510 *
29511 * <p>Notes: <ol>
29512 *
29513 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
29514 * convenient way between the two arguments. For example,
29515 * JD(TT)=2450123.7 could be expressed in any of these ways,
29516 * among others:
29517 *
29518 * date1 date2
29519 *
29520 * 2450123.7 0.0 (JD method)
29521 * 2451545.0 -1421.3 (J2000 method)
29522 * 2400000.5 50123.2 (MJD method)
29523 * 2450123.5 0.2 (date & time method)
29524 *
29525 * The JD method is the most natural and convenient to use in
29526 * cases where the loss of several decimal digits of resolution
29527 * is acceptable. The J2000 method is best matched to the way
29528 * the argument is handled internally and will deliver the
29529 * optimum resolution. The MJD method and the date & time methods
29530 * are both good compromises between resolution and convenience.
29531 *
29532 * <li> The matrix is in the sense
29533 *
29534 * E_ep = rm x P_ICRS,
29535 *
29536 * where P_ICRS is a vector with respect to ICRS right ascension
29537 * and declination axes and E_ep is the same vector with respect to
29538 * the (inertial) ecliptic and equinox of date.
29539 *
29540 * <li> P_ICRS is a free vector, merely a direction, typically of unit
29541 * magnitude, and not bound to any particular spatial origin, such
29542 * as the Earth, Sun or SSB. No assumptions are made about whether
29543 * it represents starlight and embodies astrometric effects such as
29544 * parallax or aberration. The transformation is approximately that
29545 * between mean J2000.0 right ascension and declination and ecliptic
29546 * longitude and latitude, with only frame bias (always less than
29547 * 25 mas) to disturb this classical picture.
29548 * </ol>
29549 * Called: <ul>
29550 * <li>{@link #jauObl06} mean obliquity, IAU 2006
29551 * <li>{@link #jauPmat06} PB matrix, IAU 2006
29552 * <li>{@link #jauIr} initialize r-matrix to identity
29553 * <li>{@link #jauRx} rotate around X-axis
29554 * <li>{@link #jauRxr} product of two r-matrices
29555 *</ul>
29556 *
29557 * @version 2015 December 11
29558 *
29559 * @since JSOFA release 20160503
29560 *
29561 * <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
29562 */
29563 public static double[][] jauEcm06(double date1, double date2)
29564 {
29565 double ob, e[][] = new double[3][3];
29566
29567
29568 /* Obliquity, IAU 2006. */
29569 ob = jauObl06(date1, date2);
29570
29571 /* Precession-bias matrix, IAU 2006. */
29572 double bp[][] = jauPmat06(date1, date2);
29573
29574 /* Equatorial of date to ecliptic matrix. */
29575 jauIr(e);
29576 jauRx(ob, e);
29577
29578 /* ICRS to ecliptic coordinates rotation matrix, IAU 2006. */
29579 return jauRxr(e, bp);
29580
29581 }
29582
29583 /**
29584 *
29585 * Transformation from ICRS equatorial coordinates to ecliptic
29586 * coordinates (mean equinox and ecliptic of date) using IAU 2006
29587 * precession model.
29588 *
29589 * <p>This function is derived from the International Astronomical Union's
29590 * SOFA (Standards of Fundamental Astronomy) software collection.
29591 *
29592 * <p>Status: support function.
29593 *
29594 * <!-- Given: -->
29595 * @param date1 double TT as a 2-part Julian date (Note 1)
29596 * @param date2 double TT as a 2-part Julian date (Note 1)
29597 * @param dr double ICRS right ascension and declination (radians)
29598 * @param dd double ICRS right ascension and declination (radians)
29599 *
29600 * <!-- Returned: -->
29601 * @return double ecliptic longitude and latitude (radians)
29602 *<ol>
29603 * <li> The TT date date1+date2 is a Julian Date, apportioned in any
29604 * convenient way between the two arguments. For example,
29605 * JD(TT)=2450123.7 could be expressed in any of these ways,
29606 * among others:
29607 *
29608 * date1 date2
29609 *
29610 * 2450123.7 0.0 (JD method)
29611 * 2451545.0 -1421.3 (J2000 method)
29612 * 2400000.5 50123.2 (MJD method)
29613 * 2450123.5 0.2 (date & time method)
29614 *
29615 * The JD method is the most natural and convenient to use in
29616 * cases where the loss of several decimal digits of resolution
29617 * is acceptable. The J2000 method is best matched to the way
29618 * the argument is handled internally and will deliver the
29619 * optimum resolution. The MJD method and the date & time methods
29620 * are both good compromises between resolution and convenience.
29621 *
29622 * <li> No assumptions are made about whether the coordinates represent
29623 * starlight and embody astrometric effects such as parallax or
29624 * aberration.
29625 *
29626 * <li> The transformation is approximately that from mean J2000.0 right
29627 * ascension and declination to ecliptic longitude and latitude
29628 * (mean equinox and ecliptic of date), with only frame bias (always
29629 * less than 25 mas) to disturb this classical picture.
29630 *</ol>
29631 * Called:<ul>
29632 * <li>{@link #jauS2c} spherical coordinates to unit vector
29633 * <li>{@link #jauEcm06} J2000.0 to ecliptic rotation matrix, IAU 2006
29634 * <li>{@link #jauRxp} product of r-matrix and p-vector
29635 * <li>{@link #jauC2s} unit vector to spherical coordinates
29636 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
29637 * <li>{@link #jauAnpm} normalize angle into range +/- pi
29638 *</ul>
29639 * @version 2016 February 9
29640 *
29641 * @since JSOFA release 20160503
29642 *
29643 * <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
29644 */
29645 public static SphericalCoordinate jauEqec06(double date1, double date2, double dr, double dd)
29646 {
29647
29648 /* Spherical to Cartesian. */
29649 double v1[] = jauS2c(dr, dd);
29650
29651 /* Rotation matrix, ICRS equatorial to ecliptic. */
29652 double rm[][] = jauEcm06(date1, date2);
29653
29654 /* The transformation from ICRS to ecliptic. */
29655 double v2[] = jauRxp(rm, v1);
29656
29657 /* Cartesian to spherical. */
29658 SphericalCoordinate co = jauC2s(v2);
29659
29660 /* Express in conventional ranges. */
29661 co.alpha = jauAnp(co.alpha);
29662 co.delta = jauAnpm(co.delta);
29663 return co;
29664
29665 }
29666
29667 /**
29668 *
29669 * Transformation from ecliptic coordinates (mean equinox and ecliptic
29670 * of date) to ICRS RA,Dec, using a long-term precession model.
29671 *
29672 * <p>This function is derived from the International Astronomical Union's
29673 * SOFA (Standards of Fundamental Astronomy) software collection.
29674 *
29675 * <p>Status: support function.
29676 *
29677 * <!-- Given: -->
29678 * @param epj double Julian epoch (TT)
29679 * @param dl double ecliptic longitude and latitude (radians)
29680 * @param db double ecliptic longitude and latitude (radians)
29681 *
29682 * <!-- Returned: -->
29683 * @return double ICRS right ascension and declination (radians)
29684 *<ol>
29685 * <li> No assumptions are made about whether the coordinates represent
29686 * starlight and embody astrometric effects such as parallax or
29687 * aberration.
29688 *
29689 * <li> The transformation is approximately that from ecliptic longitude
29690 * and latitude (mean equinox and ecliptic of date) to mean J2000.0
29691 * right ascension and declination, with only frame bias (always
29692 * less than 25 mas) to disturb this classical picture.
29693 *
29694 * <li> The Vondrak et al. (2011, 2012) 400 millennia precession model
29695 * agrees with the IAU 2006 precession at J2000.0 and stays within
29696 * 100 microarcseconds during the 20th and 21st centuries. It is
29697 * accurate to a few arcseconds throughout the historical period,
29698 * worsening to a few tenths of a degree at the end of the
29699 * +/- 200,000 year time span.
29700 *</ol>
29701 * Called:<ul>
29702 * <li>{@link #jauS2c} spherical coordinates to unit vector
29703 * <li>{@link #jauLtecm} J2000.0 to ecliptic rotation matrix, long term
29704 * <li>{@link #jauTrxp} product of transpose of r-matrix and p-vector
29705 * <li>{@link #jauC2s} unit vector to spherical coordinates
29706 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
29707 * <li>{@link #jauAnpm} normalize angle into range +/- pi
29708 *</ul>
29709 * References: <ul>
29710 *
29711 * <li>Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
29712 * expressions, valid for long time intervals, Astron.Astrophys. 534,
29713 * A22
29714 *
29715 * <li>Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
29716 * expressions, valid for long time intervals (Corrigendum),
29717 * Astron.Astrophys. 541, C1
29718 *</ul>
29719 * @version 2016 February 9
29720 *
29721 * @since JSOFA release 20160503
29722 *
29723 * <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
29724 */
29725 public static SphericalCoordinate jauLteceq(double epj, double dl, double db)
29726 {
29727
29728 /* Spherical to Cartesian. */
29729 double v1[] = jauS2c(dl, db);
29730
29731 /* Rotation matrix, ICRS equatorial to ecliptic. */
29732 double rm[][] = jauLtecm(epj);
29733
29734 /* The transformation from ecliptic to ICRS. */
29735 double v2[] = jauTrxp(rm, v1);
29736
29737 /* Cartesian to spherical. */
29738 SphericalCoordinate co = jauC2s(v2);
29739
29740 /* Express in conventional ranges. */
29741 co.alpha = jauAnp(co.alpha);
29742 co.delta = jauAnpm(co.delta);
29743 return co;
29744
29745 }
29746
29747 /**
29748 *
29749 * ICRS equatorial to ecliptic rotation matrix, long-term.
29750 *
29751 * <p>This function is derived from the International Astronomical Union's
29752 * SOFA (Standards of Fundamental Astronomy) software collection.
29753 *
29754 * <p>Status: support function.
29755 *
29756 * <!-- Given: -->
29757 * @param epj double Julian epoch (TT)
29758 *
29759 * <!-- Returned: -->
29760 * @return double[3][3] ICRS to ecliptic rotation matrix
29761 *
29762 * <p>Notes: <ol>
29763 *
29764 * <li> The matrix is in the sense
29765 *
29766 * E_ep = rm x P_ICRS,
29767 *
29768 * where P_ICRS is a vector with respect to ICRS right ascension
29769 * and declination axes and E_ep is the same vector with respect to
29770 * the (inertial) ecliptic and equinox of epoch epj.
29771 *
29772 * <li> P_ICRS is a free vector, merely a direction, typically of unit
29773 * magnitude, and not bound to any particular spatial origin, such
29774 * as the Earth, Sun or SSB. No assumptions are made about whether
29775 * it represents starlight and embodies astrometric effects such as
29776 * parallax or aberration. The transformation is approximately that
29777 * between mean J2000.0 right ascension and declination and ecliptic
29778 * longitude and latitude, with only frame bias (always less than
29779 * 25 mas) to disturb this classical picture.
29780 *
29781 * <li> The Vondrak et al. (2011, 2012) 400 millennia precession model
29782 * agrees with the IAU 2006 precession at J2000.0 and stays within
29783 * 100 microarcseconds during the 20th and 21st centuries. It is
29784 * accurate to a few arcseconds throughout the historical period,
29785 * worsening to a few tenths of a degree at the end of the
29786 * +/- 200,000 year time span.
29787 *</ol>
29788 * Called:<ul>
29789 * <li>{@link #jauLtpequ} equator pole, long term
29790 * <li>{@link #jauLtpecl} ecliptic pole, long term
29791 * <li>{@link #jauPxp} vector product
29792 * <li>{@link #jauPn} normalize vector
29793 *</ul>
29794 * References:<ul>
29795 *
29796 * <li>Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
29797 * expressions, valid for long time intervals, Astron.Astrophys. 534,
29798 * A22
29799 *
29800 * <li>Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
29801 * expressions, valid for long time intervals (Corrigendum),
29802 * Astron.Astrophys. 541, C1
29803 *</ul>
29804 * @version 2015 December 6
29805 *
29806 * @since JSOFA release 20160503
29807 *
29808 * <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
29809 */
29810 public static double[][] jauLtecm(double epj)
29811 {
29812 double rm[][] = new double[3][3];
29813 /* Frame bias (IERS Conventions 2010, Eqs. 5.21 and 5.33) */
29814 final double dx = -0.016617 * DAS2R,
29815 de = -0.0068192 * DAS2R,
29816 dr = -0.0146 * DAS2R;
29817
29818
29819 /* Equator pole. */
29820 double p[] = jauLtpequ(epj);
29821
29822 /* Ecliptic pole (bottom row of equatorial to ecliptic matrix). */
29823 double z[] = jauLtpecl(epj);
29824
29825 /* Equinox (top row of matrix). */
29826 double w[] = jauPxp(p, z);
29827 NormalizedVector nv = jauPn(w);
29828
29829 double x[] = nv.u;
29830 /* Middle row of matrix. */
29831 double y[] = jauPxp(z, x);
29832
29833 /* Combine with frame bias. */
29834 rm[0][0] = x[0] - x[1]*dr + x[2]*dx;
29835 rm[0][1] = x[0]*dr + x[1] + x[2]*de;
29836 rm[0][2] = - x[0]*dx - x[1]*de + x[2];
29837 rm[1][0] = y[0] - y[1]*dr + y[2]*dx;
29838 rm[1][1] = y[0]*dr + y[1] + y[2]*de;
29839 rm[1][2] = - y[0]*dx - y[1]*de + y[2];
29840 rm[2][0] = z[0] - z[1]*dr + z[2]*dx;
29841 rm[2][1] = z[0]*dr + z[1] + z[2]*de;
29842 rm[2][2] = - z[0]*dx - z[1]*de + z[2];
29843
29844 return rm;
29845
29846 }
29847
29848 /**
29849 *
29850 * Transformation from ICRS equatorial coordinates to ecliptic
29851 * coordinates (mean equinox and ecliptic of date) using a long-term
29852 * precession model.
29853 *
29854 * <p>This function is derived from the International Astronomical Union's
29855 * SOFA (Standards of Fundamental Astronomy) software collection.
29856 *
29857 * <p>Status: support function.
29858 *
29859 * <!-- Given: -->
29860 * @param epj double Julian epoch (TT)
29861 * @param dr,dd double ICRS right ascension and declination (radians)
29862 *
29863 * <!-- Returned: -->
29864 * @return ecliptic longitude and latitude (radians)
29865 *<ol>
29866 * <li> No assumptions are made about whether the coordinates represent
29867 * starlight and embody astrometric effects such as parallax or
29868 * aberration.
29869 *
29870 * <li> The transformation is approximately that from mean J2000.0 right
29871 * ascension and declination to ecliptic longitude and latitude
29872 * (mean equinox and ecliptic of date), with only frame bias (always
29873 * less than 25 mas) to disturb this classical picture.
29874 *
29875 * <li> The Vondrak et al. (2011, 2012) 400 millennia precession model
29876 * agrees with the IAU 2006 precession at J2000.0 and stays within
29877 * 100 microarcseconds during the 20th and 21st centuries. It is
29878 * accurate to a few arcseconds throughout the historical period,
29879 * worsening to a few tenths of a degree at the end of the
29880 * +/- 200,000 year time span.
29881 *</ol>
29882 * Called:<ul>
29883 * <li>{@link #jauS2c} spherical coordinates to unit vector
29884 * <li>{@link #jauLtecm} J2000.0 to ecliptic rotation matrix, long term
29885 * <li>{@link #jauRxp} product of r-matrix and p-vector
29886 * <li>{@link #jauC2s} unit vector to spherical coordinates
29887 * <li>{@link #jauAnp} normalize angle into range 0 to 2pi
29888 * <li>{@link #jauAnpm} normalize angle into range +/- pi
29889 *</ul>
29890 * References:
29891 *
29892 * Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
29893 * expressions, valid for long time intervals, Astron.Astrophys. 534,
29894 * A22
29895 *
29896 * Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
29897 * expressions, valid for long time intervals (Corrigendum),
29898 * Astron.Astrophys. 541, C1
29899 *
29900 * @version 2016 February 9
29901 *
29902 * @since JSOFA release 20160503
29903 *
29904 * <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
29905 */
29906 public static SphericalCoordinate jauLteqec(double epj, double dr, double dd)
29907 {
29908
29909 /* Spherical to Cartesian. */
29910 double v1[] = jauS2c(dr, dd);
29911
29912 /* Rotation matrix, ICRS equatorial to ecliptic. */
29913 double rm[][] = jauLtecm(epj);
29914
29915 /* The transformation from ICRS to ecliptic. */
29916 double v2[] = jauRxp(rm, v1);
29917
29918 /* Cartesian to spherical. */
29919 SphericalCoordinate co = jauC2s(v2);
29920
29921 /* Express in conventional ranges. */
29922 co.alpha = jauAnp(co.alpha);
29923 co.delta = jauAnpm(co.delta);
29924
29925 return co;
29926 }
29927
29928 /**
29929 *
29930 * Long-term precession matrix.
29931 *
29932 * <p>This function is derived from the International Astronomical Union's
29933 * SOFA (Standards of Fundamental Astronomy) software collection.
29934 *
29935 * <p>Status: support function.
29936 *
29937 * <!-- Given: -->
29938 * @param epj double Julian epoch (TT)
29939 *
29940 * <!-- Returned: -->
29941 * @return double[3][3] precession matrix, J2000.0 to date
29942 *
29943 * <p>Notes: <ol>
29944 *
29945 * <li> The matrix is in the sense
29946 *
29947 * P_date = rp x P_J2000,
29948 *
29949 * where P_J2000 is a vector with respect to the J2000.0 mean
29950 * equator and equinox and P_date is the same vector with respect to
29951 * the equator and equinox of epoch epj.
29952 *
29953 * <li> The Vondrak et al. (2011, 2012) 400 millennia precession model
29954 * agrees with the IAU 2006 precession at J2000.0 and stays within
29955 * 100 microarcseconds during the 20th and 21st centuries. It is
29956 * accurate to a few arcseconds throughout the historical period,
29957 * worsening to a few tenths of a degree at the end of the
29958 * +/- 200,000 year time span.
29959 *</ol>
29960 * Called:<ul>
29961 * <li>{@link #jauLtpequ} equator pole, long term
29962 * <li>{@link #jauLtpecl} ecliptic pole, long term
29963 * <li>{@link #jauPxp} vector product
29964 * <li>{@link #jauPn} normalize vector
29965 *</ul>
29966 * References:
29967 *
29968 * <p>Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
29969 * expressions, valid for long time intervals, Astron.Astrophys. 534,
29970 * A22
29971 *
29972 * <p>Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
29973 * expressions, valid for long time intervals (Corrigendum),
29974 * Astron.Astrophys. 541, C1
29975 *
29976 * @version 2015 December 6
29977 *
29978 * @since JSOFA release 20160503
29979 *
29980 * <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
29981 */
29982 public static double[][] jauLtp(double epj )
29983 {
29984 double rp[][] = new double[3][3];
29985 int i;
29986
29987
29988
29989 /* Equator pole (bottom row of matrix). */
29990 double peqr[] = jauLtpequ(epj);
29991
29992 /* Ecliptic pole. */
29993 double pecl[] = jauLtpecl(epj);
29994
29995 /* Equinox (top row of matrix). */
29996 double v[] = jauPxp(peqr, pecl);
29997 NormalizedVector nv = jauPn(v);
29998
29999 /* Middle row of matrix. */
30000 v = jauPxp(peqr, nv.u);
30001
30002 /* Assemble the matrix. */
30003 for ( i = 0; i < 3; i++ ) {
30004 rp[0][i] = nv.u[i];
30005 rp[1][i] = v[i];
30006 rp[2][i] = peqr[i];
30007 }
30008
30009 return rp;
30010 }
30011
30012
30013 /**
30014 *
30015 * Long-term precession matrix, including ICRS frame bias.
30016 *
30017 * <p>This function is derived from the International Astronomical Union's
30018 * SOFA (Standards of Fundamental Astronomy) software collection.
30019 *
30020 * <p>Status: support function.
30021 *
30022 * <!-- Given: -->
30023 * @param epj double Julian epoch (TT)
30024 *
30025 * <!-- Returned: -->
30026 * @return double[3][3] precession-bias matrix, J2000.0 to date
30027 *
30028 * <p>Notes: <ol>
30029 *
30030 * <li> The matrix is in the sense
30031 *
30032 * P_date = rpb x P_ICRS,
30033 *
30034 * where P_ICRS is a vector in the Geocentric Celestial Reference
30035 * System, and P_date is the vector with respect to the Celestial
30036 * Intermediate Reference System at that date but with nutation
30037 * neglected.
30038 *
30039 * <li> A first order frame bias formulation is used, of sub-
30040 * microarcsecond accuracy compared with a full 3D rotation.
30041 *
30042 * <li> The Vondrak et al. (2011, 2012) 400 millennia precession model
30043 * agrees with the IAU 2006 precession at J2000.0 and stays within
30044 * 100 microarcseconds during the 20th and 21st centuries. It is
30045 * accurate to a few arcseconds throughout the historical period,
30046 * worsening to a few tenths of a degree at the end of the
30047 * +/- 200,000 year time span.
30048 *</ol>
30049 * References:
30050 *
30051 * Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
30052 * expressions, valid for long time intervals, Astron.Astrophys. 534,
30053 * A22
30054 *
30055 * Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
30056 * expressions, valid for long time intervals (Corrigendum),
30057 * Astron.Astrophys. 541, C1
30058 *
30059 * @version 2015 December 6
30060 *
30061 * @since JSOFA release 20160503
30062 *
30063 * <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
30064 */
30065 public static double[][] jauLtpb(double epj)
30066 {
30067 double rpb[][] = new double[3][3];
30068 /* Frame bias (IERS Conventions 2010, Eqs. 5.21 and 5.33) */
30069 final double dx = -0.016617 * DAS2R,
30070 de = -0.0068192 * DAS2R,
30071 dr = -0.0146 * DAS2R;
30072
30073 int i;
30074
30075
30076
30077 /* Precession matrix. */
30078 double rp[][] = jauLtp(epj);
30079
30080 /* Apply the bias. */
30081 for ( i = 0; i < 3; i++ ) {
30082 rpb[i][0] = rp[i][0] - rp[i][1]*dr + rp[i][2]*dx;
30083 rpb[i][1] = rp[i][0]*dr + rp[i][1] + rp[i][2]*de;
30084 rpb[i][2] = -rp[i][0]*dx - rp[i][1]*de + rp[i][2];
30085 }
30086
30087 return rpb;
30088 }
30089
30090 /**
30091 *
30092 * Long-term precession of the ecliptic.
30093 *
30094 * <p>This function is derived from the International Astronomical Union's
30095 * SOFA (Standards of Fundamental Astronomy) software collection.
30096 *
30097 * <p>Status: support function.
30098 *
30099 * <!-- Given: -->
30100 * @param epj double Julian epoch (TT)
30101 *
30102 * <!-- Returned: -->
30103 * @return double[3] ecliptic pole unit vector
30104 *
30105 * <p>Notes: <ol>
30106 *
30107 * <li> The returned vector is with respect to the J2000.0 mean equator
30108 * and equinox.
30109 *
30110 * <li> The Vondrak et al. (2011, 2012) 400 millennia precession model
30111 * agrees with the IAU 2006 precession at J2000.0 and stays within
30112 * 100 microarcseconds during the 20th and 21st centuries. It is
30113 * accurate to a few arcseconds throughout the historical period,
30114 * worsening to a few tenths of a degree at the end of the
30115 * +/- 200,000 year time span.
30116 *</ol>
30117 * References:
30118 *
30119 * Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
30120 * expressions, valid for long time intervals, Astron.Astrophys. 534,
30121 * A22
30122 *
30123 * Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
30124 * expressions, valid for long time intervals (Corrigendum),
30125 * Astron.Astrophys. 541, C1
30126 *
30127 * @version 2016 February 9
30128 *
30129 * @since JSOFA release 20160503
30130 *
30131 * <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
30132 */
30133 public static double[] jauLtpecl(double epj)
30134 {
30135
30136 double vec[] = new double[3];
30137 /* Obliquity at J2000.0 (radians). */
30138 final double eps0 = 84381.406 * DAS2R;
30139
30140 /* Polynomial coefficients */
30141 final int NPOL = 4 ;
30142 final double pqpol[][] = {
30143 { 5851.607687,
30144 -0.1189000,
30145 -0.00028913,
30146 0.000000101},
30147 {-1600.886300,
30148 1.1689818,
30149 -0.00000020,
30150 -0.000000437}
30151 };
30152
30153 /* Periodic coefficients */
30154 final double pqper[][] = {
30155 { 708.15,-5486.751211,-684.661560, 667.666730,-5523.863691},
30156 {2309.00, -17.127623,2446.283880,-2354.886252, -549.747450},
30157 {1620.00, -617.517403, 399.671049, -428.152441, -310.998056},
30158 { 492.20, 413.442940,-356.652376, 376.202861, 421.535876},
30159 {1183.00, 78.614193,-186.387003, 184.778874, -36.776172},
30160 { 622.00, -180.732815,-316.800070, 335.321713, -145.278396},
30161 { 882.00, -87.676083, 198.296701, -185.138669, -34.744450},
30162 { 547.00, 46.140315, 101.135679, -120.972830, 22.885731}
30163 };
30164 final int NPER = pqper.length;
30165
30166 /* Miscellaneous */
30167 int i;
30168 double t, p, q, w, a, s, c;
30169
30170
30171 /* Centuries since J2000. */
30172 t = ( epj - 2000.0 ) / 100.0;
30173
30174 /* Initialize P_A and Q_A accumulators. */
30175 p = 0.0;
30176 q = 0.0;
30177
30178 /* Periodic terms. */
30179 w = D2PI*t;
30180 for ( i = 0; i < NPER; i++ ) {
30181 a = w/pqper[i][0];
30182 s = sin(a);
30183 c = cos(a);
30184 p += c*pqper[i][1] + s*pqper[i][3];
30185 q += c*pqper[i][2] + s*pqper[i][4];
30186 }
30187
30188 /* Polynomial terms. */
30189 w = 1.0;
30190 for ( i = 0; i < NPOL; i++ ) {
30191 p += pqpol[0][i]*w;
30192 q += pqpol[1][i]*w;
30193 w *= t;
30194 }
30195
30196 /* P_A and Q_A (radians). */
30197 p *= DAS2R;
30198 q *= DAS2R;
30199
30200 /* Form the ecliptic pole vector. */
30201 w = 1.0 - p*p - q*q;
30202 w = w < 0.0 ? 0.0 : sqrt(w);
30203 s = sin(eps0);
30204 c = cos(eps0);
30205 vec[0] = p;
30206 vec[1] = - q*c - w*s;
30207 vec[2] = - q*s + w*c;
30208
30209 return vec;
30210
30211 }
30212
30213 /**
30214 *
30215 * Long-term precession of the equator.
30216 *
30217 * <p>This function is derived from the International Astronomical Union's
30218 * SOFA (Standards of Fundamental Astronomy) software collection.
30219 *
30220 * <p>Status: support function.
30221 *
30222 * <!-- Given: -->
30223 * @param epj double Julian epoch (TT)
30224 *
30225 * <!-- Returned: -->
30226 * @return double[3] equator pole unit vector
30227 *
30228 * <p>Notes: <ol>
30229 *
30230 * <li> The returned vector is with respect to the J2000.0 mean equator
30231 * and equinox.
30232 *
30233 * <li> The Vondrak et al. (2011, 2012) 400 millennia precession model
30234 * agrees with the IAU 2006 precession at J2000.0 and stays within
30235 * 100 microarcseconds during the 20th and 21st centuries. It is
30236 * accurate to a few arcseconds throughout the historical period,
30237 * worsening to a few tenths of a degree at the end of the
30238 * +/- 200,000 year time span.
30239 *</ol>
30240 * References:
30241 *
30242 * Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
30243 * expressions, valid for long time intervals, Astron.Astrophys. 534,
30244 * A22
30245 *
30246 * Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
30247 * expressions, valid for long time intervals (Corrigendum),
30248 * Astron.Astrophys. 541, C1
30249 *
30250 * @version 2016 February 9
30251 *
30252 * @since JSOFA release 20160503
30253 *
30254 * <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
30255 */
30256 public static double[] jauLtpequ(double epj)
30257 {
30258 double veq[] = new double[3];
30259 /* Polynomial coefficients */
30260 final int NPOL = 4;
30261 final double xypol[][] = {
30262 { 5453.282155,
30263 0.4252841,
30264 -0.00037173,
30265 -0.000000152},
30266 {-73750.930350,
30267 -0.7675452,
30268 -0.00018725,
30269 0.000000231}
30270 };
30271
30272 /* Periodic coefficients */
30273 final double xyper[][] = {
30274 { 256.75, -819.940624,75004.344875,81491.287984, 1558.515853},
30275 { 708.15,-8444.676815, 624.033993, 787.163481, 7774.939698},
30276 { 274.20, 2600.009459, 1251.136893, 1251.296102,-2219.534038},
30277 { 241.45, 2755.175630,-1102.212834,-1257.950837,-2523.969396},
30278 {2309.00, -167.659835,-2660.664980,-2966.799730, 247.850422},
30279 { 492.20, 871.855056, 699.291817, 639.744522, -846.485643},
30280 { 396.10, 44.769698, 153.167220, 131.600209,-1393.124055},
30281 { 288.90, -512.313065, -950.865637, -445.040117, 368.526116},
30282 { 231.10, -819.415595, 499.754645, 584.522874, 749.045012},
30283 {1610.00, -538.071099, -145.188210, -89.756563, 444.704518},
30284 { 620.00, -189.793622, 558.116553, 524.429630, 235.934465},
30285 { 157.87, -402.922932, -23.923029, -13.549067, 374.049623},
30286 { 220.30, 179.516345, -165.405086, -210.157124, -171.330180},
30287 {1200.00, -9.814756, 9.344131, -44.919798, -22.899655}
30288 };
30289 final int NPER = xyper.length;
30290
30291 /* Miscellaneous */
30292 int i;
30293 double t, x, y, w, a, s, c;
30294
30295
30296 /* Centuries since J2000. */
30297 t = ( epj - 2000.0 ) / 100.0;
30298
30299 /* Initialize X and Y accumulators. */
30300 x = 0.0;
30301 y = 0.0;
30302
30303 /* Periodic terms. */
30304 w = D2PI * t;
30305 for ( i = 0; i < NPER; i++ ) {
30306 a = w / xyper[i][0];
30307 s = sin(a);
30308 c = cos(a);
30309 x += c*xyper[i][1] + s*xyper[i][3];
30310 y += c*xyper[i][2] + s*xyper[i][4];
30311 }
30312
30313 /* Polynomial terms. */
30314 w = 1.0;
30315 for ( i = 0; i < NPOL; i++ ) {
30316 x += xypol[0][i]*w;
30317 y += xypol[1][i]*w;
30318 w *= t;
30319 }
30320
30321 /* X and Y (direction cosines). */
30322 x *= DAS2R;
30323 y *= DAS2R;
30324
30325 /* Form the equator pole vector. */
30326 veq[0] = x;
30327 veq[1] = y;
30328 w = 1.0 - x*x - y*y;
30329 veq[2] = w < 0.0 ? 0.0 : sqrt(w);
30330
30331
30332 return veq;
30333
30334 }
30335
30336 }
30337
30338 /*
30339 * Copyright © 2016 Paul Harrison, University of Manchester.
30340 *
30341 * This JSOFA software is derived from the official C release of the "Standards Of Fundamental Astronomy" (SOFA) library
30342 * of the International Astronomical Union. The intention is to reproduce the functionality and algorithms of
30343 * the official SOFA library in a pure Java form.
30344 *
30345 * The responsibility for the maintenance and supply of the JSOFA library lies with the author (not the IAU SOFA Board),
30346 * However, The JSOFA software is provided "as is" and the author makes no warranty as to its use or performance.
30347 * The author does not and cannot warrant the performance or results which the user may obtain by using the JSOFA software.
30348 * The author makes no warranties, express or implied, as to non-infringement of third party rights, merchantability,
30349 * or fitness for any particular purpose. In no event will the author be liable to the user for any consequential,
30350 * incidental, or special damages, including any lost profits or lost savings, even if the author has been advised
30351 * of such damages, or for any claim by any third party.
30352 *
30353 * Other conditions of the original license (reproduced below) are carried over as applicable.
30354 */
30355
30356 /*----------------------------------------------------------------------
30357 **
30358 ** Copyright (C) 2016
30359 ** Standards Of Fundamental Astronomy Board
30360 ** of the International Astronomical Union.
30361 **
30362 ** =====================
30363 ** SOFA Software License
30364 ** =====================
30365 **
30366 ** NOTICE TO USER:
30367 **
30368 ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
30369 ** CONDITIONS WHICH APPLY TO ITS USE.
30370 **
30371 ** 1. The Software is owned by the IAU SOFA Board ("SOFA").
30372 **
30373 ** 2. Permission is granted to anyone to use the SOFA software for any
30374 ** purpose, including commercial applications, free of charge and
30375 ** without payment of royalties, subject to the conditions and
30376 ** restrictions listed below.
30377 **
30378 ** 3. You (the user) may copy and distribute SOFA source code to others,
30379 ** and use and adapt its code and algorithms in your own software,
30380 ** on a world-wide, royalty-free basis. That portion of your
30381 ** distribution that does not consist of intact and unchanged copies
30382 ** of SOFA source code files is a "derived work" that must comply
30383 ** with the following requirements:
30384 **
30385 ** a) Your work shall be marked or carry a statement that it
30386 ** (i) uses routines and computations derived by you from
30387 ** software provided by SOFA under license to you; and
30388 ** (ii) does not itself constitute software provided by and/or
30389 ** endorsed by SOFA.
30390 **
30391 ** b) The source code of your derived work must contain descriptions
30392 ** of how the derived work is based upon, contains and/or differs
30393 ** from the original SOFA software.
30394 **
30395 ** c) The names of all routines in your derived work shall not
30396 ** include the prefix "iau" or "sofa" or trivial modifications
30397 ** thereof such as changes of case.
30398 **
30399 ** d) The origin of the SOFA components of your derived work must
30400 ** not be misrepresented; you must not claim that you wrote the
30401 ** original software, nor file a patent application for SOFA
30402 ** software or algorithms embedded in the SOFA software.
30403 **
30404 ** e) These requirements must be reproduced intact in any source
30405 ** distribution and shall apply to anyone to whom you have
30406 ** granted a further right to modify the source code of your
30407 ** derived work.
30408 **
30409 ** Note that, as originally distributed, the SOFA software is
30410 ** intended to be a definitive implementation of the IAU standards,
30411 ** and consequently third-party modifications are discouraged. All
30412 ** variations, no matter how minor, must be explicitly marked as
30413 ** such, as explained above.
30414 **
30415 ** 4. You shall not cause the SOFA software to be brought into
30416 ** disrepute, either by misuse, or use for inappropriate tasks, or
30417 ** by inappropriate modification.
30418 **
30419 ** 5. The SOFA software is provided "as is" and SOFA makes no warranty
30420 ** as to its use or performance. SOFA does not and cannot warrant
30421 ** the performance or results which the user may obtain by using the
30422 ** SOFA software. SOFA makes no warranties, express or implied, as
30423 ** to non-infringement of third party rights, merchantability, or
30424 ** fitness for any particular purpose. In no event will SOFA be
30425 ** liable to the user for any consequential, incidental, or special
30426 ** damages, including any lost profits or lost savings, even if a
30427 ** SOFA representative has been advised of such damages, or for any
30428 ** claim by any third party.
30429 **
30430 ** 6. The provision of any version of the SOFA software under the terms
30431 ** and conditions specified herein does not imply that future
30432 ** versions will also be made available under the same terms and
30433 ** conditions.
30434 *
30435 ** In any published work or commercial product which uses the SOFA
30436 ** software directly, acknowledgement (see www.iausofa.org) is
30437 ** appreciated.
30438 **
30439 ** Correspondence concerning SOFA software should be addressed as
30440 ** follows:
30441 **
30442 ** By email: sofa@ukho.gov.uk
30443 ** By post: IAU SOFA Center
30444 ** HM Nautical Almanac Office
30445 ** UK Hydrographic Office
30446 ** Admiralty Way, Taunton
30447 ** Somerset, TA1 2DN
30448 ** United Kingdom
30449 **
30450 **--------------------------------------------------------------------*/
30451
30452
30453 /*
30454 * $Log$
30455 */